Preheat oven to 365 degrees Fahrenheit
Add almond paste to a food processor and break up a bit to form little balls. Then add ¾ cup sugar and process until combined. About 1 min.
With the whisk attachment, beat egg whites in a standing mixer at med-high speed until soft peaks form. While running, slowly add ¼ cup sugar. Beat until glossy, stiff peaks form. Transfer to another bowl and wipe original bowl clean.
Change the whisk attachment to the paddle. Add the almond paste mixture and butter to the bowl and beat until pale and fluffy, about 3 mins. Add yolks, almond extract, vanilla extract and beat until well combined. Reduce speed to low and add salt and flour. Mix until just combined.
Add a little of the egg whites to moisten dough. Then all rest of egg whites and gently fold in.
Divide batter into 3 bowls. Add red coloring to one, green to another and keep the last plain.
Pour batter into the three pans (no need to grease bc of all the butter but you can spray if it makes you feel better). Even out batter. These will look thin. Don't worry.
Bake for 10-12 minutes or until just set. Remove and let fully cool.
Add parchment paper to a baking sheet and flip the red layer onto it. Spread a thin layer of apricot preserves on top, removing big pieces. Flip the white layer and add raspberry jam. Flip the green layer. (If your cake breaks or cracks, just puzzle it together. It all gets smooshed together so don't worry).
Wrap tightly in plastic wrap then add another baking sheet on top and weigh down with cook books or cans. Refrigerate overnight.
Unwrap cake. Temper the chocolate by adding ¾ cup of chocolate chips to a bowl and microwave in 20 second bursts until melted (3-4 times). Add the ¼ cup chocolate chips to the melted chocolate and stir until those are melted, then add back to the microwave for JUST 20 seconds. Spread on top of cake and refrigerate until set (30 mins).
Add parchment paper to another baking sheet and flip cake on top. Repeat chocolate process and set one hour.
Flip cake onto a cutting board. Let serrated knife sit in hot-to-boiling water. Trim off ends then gently cut cookies out.