six 8-inch round cake pans; a candy thermometer; a piping bag fitted with a small star tip; an offset spatula; a bench scraper or frosting smoother; rubber gloves; a 1 1/2-inch triangle cutter
For the cake layers: Preheat the oven to 350 degrees F. Coat six 8-inch round cake pans with flour-based baking spray (or grease and flour pans).
Sift the flour, baking powder and salt into a large bowl. Combine the milk and vanilla in a large liquid measure with a pour spout. Beat the butter in the bowl of an electric mixer on medium speed until smooth. With the mixer running, gradually add the granulated sugar and beat until the mixture turns pale and fluffy, about 3 minutes. Reduce the speed to low and add the flour mixture in 3 additions, alternating with the milk mixture. Begin and end with the flour. Mix until just combined.
Beat the egg whites in a spotlessly clean bowl on high speed until stiff peaks form, about 5 minutes. Gently fold the egg whites into the batter in 3 additions.
Place 2 cups of the cake batter in 6 separate bowls. Tint each bowl of batter with a different gel food color, so that you have a bowl of red, orange, yellow, green, blue and violet batter. Fold the color in well with a rubber spatula until no streaks of white cake batter remain.
Spread the batter into the prepared pans and bake until a toothpick inserted in the center of the cakes comes out clean, about 20 minutes. Turn the cakes out onto wire racks to cool completely. When the cakes are cool, level the tops with a serrated knife or a cake leveler.
For the Swiss meringue buttercream: Set a saucepan filled one-third full of water over medium-high heat and bring to a simmer.
Whisk together the egg whites, granulated sugar and salt in a large heatproof bowl. Set the bowl over the simmering water and whisk until the mixture is hot to the touch and the sugar has dissolved (120 to 140 degrees F on a candy thermometer). Transfer the mixture to the bowl of an electric mixer fitted with the whisk attachment. Beat on low speed for 2 minutes. Increase to medium high until stiff peaks form. Continue beating at medium-high speed until the mixture is fluffy and has cooled (the mixing bowl should feel cool to the touch).
Turn the mixer off and switch from the whisk attachment to the paddle. Turn the mixer to medium-low speed and add the butter a few cubes at a time, beating until well incorporated before the next addition (see Cook's Note). Add the vanilla extract. Beat on high speed until the frosting is thick and completely smooth.
Frost the cake: Transfer 1 cup of frosting to a piping bag fitted with a small star tip; set aside.
Top each cake layer with a small amount of frosting. Begin with the violet cake layer on the bottom, followed by the blue, green, yellow, orange and red. Cover the entire cake with frosting using an offset spatula and smooth the frosting with a bench scraper or frosting smoother. Place the cake in a large dish and use a cupped hand to press on the rainbow sprinkles, allowing the excess to fall back into the dish. Repeat until the bottom two-thirds of the cake is covered with the sprinkles. Using the reserved frosting in the piping bag, pipe stars around the top edge and center of the cake, and around the bottom edge of the cake. Decorate each star on the top edge of the cake with alternating colors of the round candies. Scatter rainbow nonpareils over the bottom edge. Add more rainbow sprinkles to the top center of the cake.
For the marshmallow fondant bunting: Combine the marshmallows and 1 1/2 teaspoons water in a large microwave-safe bowl. Microwave for 30-second intervals at 100% power, stirring in between each, until melted and smooth, about 1 minute.
Add 1 cup of sifted confectioners' sugar to the melted marshmallow and stir to combine. When the first cup is thoroughly mixed in, add the second cup of confectioners' sugar. Stir well until stiff. Grease a work surface with the vegetable shortening and transfer the fondant from the bowl to the greased area. Knead well until smooth and pliable. The fondant should not be sticky and it should hold its shape firmly when rolled into a ball. If the ball relaxes and loses its shape, knead in more confectioners' sugar a little at a time.
Roll the fondant into a ball and cut into 6 even pieces. Tint each ball with the food colors so that you have one of each: red, orange, yellow, green, blue and violet. (Wear gloves during kneading to avoid staining hands.)
Roll out each piece of fondant to 1/8 inch thickness on a piece of parchment paper. Use a 1 1/2-inch triangle cutter to stamp shapes from each piece of fondant.
Place the triangles end-to-end in a swag design around the top edge of the cake, in rainbow color order (red, orange, yellow, green, blue, violet). If the pieces do not naturally stick to the frosting, add a small dot of water to the backs of the triangles to adhere them to the cake.
Serve eye-popping slices of rainbow cake to delighted guests. If there are leftovers, cover the cake loosely with plastic wrap and store at room temperature.
When making the buttercream, after a few pieces of butter are added to the whipped whites, the mixture will deflate. It may look like soup or even look curdled--do not let this discourage you. This is just one ugly stage the buttercream must pass through before becoming beautiful fluffy frosting.