For the cookies: Whisk together the flour, baking powder and salt in a medium bowl. Beat the butter and sugar in a large bowl with an electric mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in 1 egg and the vanilla until incorporated. Reduce the mixer speed to low and add the flour mixture and beat until just combined.
Turn the dough out of the bowl and bring it together. Remove 3/4 cup dough and set it aside (this will be for the cone). Put 1/2 cup of dough into a medium bowl, add the cocoa powder and mix until combined (this will be for the chocolate ice cream). Put 1 cup dough into a medium bowl, add 1 drop red food coloring and mix until combined (this will be the strawberry ice cream). Place the remaining 2 teaspoons dough into a small bowl, add 2 drops red food coloring and mix until combined (this will be the cherry).
For the cone: Lightly dust a work surface. Roll the reserved 3/4 cup uncolored dough into a 10-inch log. Press the entire length of the log into an isosceles trapezoid shape. Use a ruler to help flatten the sides and top. The top of the trapezoid should be about 1 inch wide and the bottom should be about 1/4 inch wide. The sides should be about 1 inch tall. Put the log on a piece of plastic wrap. Prop the dough up against a loaf pan with the bottom resting against the counter. Alternatively, if you have 2 loaf pans, place them upside down, next to each other lengthwise. Add a piece of plastic wrap long enough to cover both pans with a slight overhang. Press the cone dough into the plastic wrap between the pans to your trapezoid. Flatten the top.
Make the strawberry ice cream: Roll the pink dough into an 11-inch log. Use a ruler to flatten one side of the log so the log is a half-circle shape. The dough will spread as you shape it; the flat side of the log should be about 1 1/4 inches wide. Brush the flat side with the egg wash and press it on top of the cone.
Make the chocolate ice cream: Roll the chocolate dough into an 11-inch log. Use a ruler to flatten one side of the log so the log is a half-circle shape. The dough will spread as you shape it; the flat side of the log should be about 3/4 inch wide. Brush the flat side with the egg wash and press it on top of the strawberry ice cream.
Make the cherry on top: Roll the red dough into a 12-inch rope. Brush one side with egg wash and press on top of the chocolate ice cream. Wrap the entire ice cream cone in plastic wrap and freeze until hard, about 30 minutes.
Position oven racks in the upper and lower thirds of the oven. Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment.
Cut 1/4 inch off each end of the ice cream log with a very sharp knife to reveal the ice cream cone shape. Cut into 1/4-inch-thick slices. Arrange the slices about 1 1/2 inches apart on the prepared baking sheets. Bake, rotating about halfway through, until crisp and just starting to turn brown on the bottom, 10 to 12 minutes. Let the cookies cool on the baking sheet for 10 minutes before transferring to a rack to cool completely.
Make the royal icing: Meanwhile, combine the confectioners' sugar and meringue power in a large bowl. Add 2 tablespoons water and beat with an electric mixer on medium-high speed until the icing forms thick and glossy peaks, about 2 minutes (adding up to 1 tablespoon more water, if needed). Remove half of the icing to a small resealable plastic bag. Add the beige food coloring to the mixing bowl and beat on low speed until the color is incorporated. Transfer to a small resealable plastic bag. Put the chocolate chips in a small microwave-safe bowl and melt in 30 second intervals, stirring in between each, until smooth, about 1 minute. Transfer the chocolate to a third small resealable plastic bag.
Cut a very small hole in the corner of each of the plastic bags. Pipe the white icing on the chocolate ice cream to mimic whipped cream. Sprinkle with a few rainbow sprinkles. Pipe a few dots of chocolate onto the strawberry ice cream and top with a few mini chocolate chips. Pipe the beige icing in a diagonal crisscross pattern on the cone. Let the icing and chocolate harden completely at room temperature before serving, about 15 minutes.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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