For the cakes:
Position a rack in the lower third of the oven and preheat to 350 degrees F. Lightly brush 2 (9-inch) round cake pans with shortening or butter. Line bottoms with buttered parchment paper and dust with flour.
Sift the flour, baking powder, soda, and salt into a medium bowl; whisk to combine evenly. Stir the sour cream, lemon juice and vanilla together in a liquid measuring cup, and set aside.
Beat the butter in a standing mixer with the paddle attachment on high until light and creamy, about 2 minutes. Stop and scrape butter off the sides of the bowl. Continue beating while gradually adding the sugar-- it should take a couple minutes to add all the sugar. Continue beating until very light and fluffy, about 3 to 4 minutes more. Scrape down the sides of the bowl and beat in the lemon zest. Add the eggs, 1 at a time, beating well after each addition.
At low speed, add the flour mixture in 3 parts, alternating with the sour cream in 2 parts, beginning and ending with the flour. Scrape the sides of the bowl and mix for 15 seconds longer.
Divide the batter evenly between the prepared pans and smooth the top with a knife. (Lightly tap the pan on the counter so the batter settles evenly.)
Bake the cakes until a toothpick inserted in the center comes out clean, about 35 to 40 minutes. Cool in the pan on a rack for 20 minutes; then turn cakes out onto the rack to cool completely.
For the Icing:
Bring a few inches of water to a boil in a saucepan that can hold a mixer's bowl above the water. Whisk the sugar, the egg whites, lemon juice, cream of tartar, and salt in the bowl by hand. Set the bowl above the boiling water and continue whisking until the mixture is hot to the touch and the sugar dissolves, about 1 to 2 minutes. Transfer the bowl to a standing mixer fitted with the whisk attachment and beat the whites at medium-high speed until they almost holds a stiff peak and are cool, about 10 minutes. Beat in the butter, a little at a time, until the icing is smooth and spreadable. (If the icing separates, just keep beating and it will come back together.)
To assemble the cake:
Slice each cake in half horizontally with a serrated knife, to make 4 even layers, taking care that they are as flat and straight as possible.
Set a large flat plate on a large inverted bowl or bottom of a salad spinner (of course, if you have a cake stand, use that), dabbing a little frosting on the bottom of the plate to secure it. Place a cake layer top side up on the plate. Using an offset spatula spread about half of the jam in a thin layer over the first cake layer, leaving about 1/4-inch border along the outside. Lay the second cake layer on top, stacking it as straight as possible. Using an offset spatula spread about 1 cup of the icing on the top layer. Place a third cake layer on top.
Spread remaining red raspberry jam over the cake layer and place the final layer on top, pressing down lightly to secure all 4 layers together. Spread about 3/4 of the remaining icing around the sides with a knife or offset spatula, then ice the top of the cake. Use an offset spatula to smooth icing as much as possible. Press plain or iced cookies around the sides, taking care to leave space to cut the cake. Garnish with additional candied almonds and sprinkle the top of the cake with pastel colored sanding sugars. Serve immediately or set aside at room temperature for up to 2 hours before serving. If refrigerating the cake, bring to room temperature 30 minutes before serving.
Whisk the flour, baking powder, and salt in a medium bowl.
Beat the butter and both sugars in another medium bowl with an electric mixer on medium-high speed until light and fluffy, about 30 seconds. Add the eggs and vanilla mixing until fully incorporated. Slowly add the flour mixture, and continue beating just until the dough comes together, stopping and scraping down the sides of the bowl as needed.
Divide dough in half, pat into disks, wrap in plastic wrap and refrigerate until firm, at least 2 hours.
Generously flour a clean work surface. (For a nice, even layer of flour, lightly sift flour over the work surface.) Gently roll chilled dough about 1/4-inch thick. Cut into desired shape using a cookie cutter, working quickly enough so dough remains chilled. If dough gets too soft, refrigerate on a lined baking sheet until firm again, about 30 minutes.
Transfer cut cookies to un-greased baking sheets, leaving about 1-inch between cookies. Refrigerate the formed cookies for at least 30 minutes. Lightly dust off excess flour with a dry pastry brush. (Excess dough can be pressed into a disk, chilled and rerolled.)
Preheat the oven to 325 degrees F. Bake the cookies, until the bottoms are golden, about 12 to 15 minutes depending on shape. Cool on the baking sheets until firm enough to transfer to a rack to cool. Decorate as desired and serve. Store in an airtight container at room temperature for up to 1 week.
Double wrap the cake in plastic wrap and store in the freezer for up to 2 months.
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