Preheat oven to 350°F and grease three (3) 9x13-inch baking pans with olive oil. Line baking pans with parchment paper sling, pushing parchment into corners and up sides of pans.
Sift flour and salt together in medium bowl. Finely grate almond paste into a separate large bowl. Whisk in olive oil, sugar, milk, egg yolks and almond extract until light in color, about 3 to 5 minutes. Mix in dry ingredients in 3 additions, mixing well between each addition, until just combined.
Whisk egg white in large bowl until stiff peaks form, about 1 minute. Fold egg whites into batter until just combined.
Spread one-third of the batter evenly into one of the prepared baking pans. Divide remaining batter evenly between 2 medium bowls. Add food coloring to each bowl. Stir gently to combine, adjusting shades as desired.
Spread red and green batters evenly into separate prepared baking pans. Bake, rotating baking pans halfway through, until edges are light golden-brown, or until a toothpick inserted into the center comes out clean, about 12 to 15 minutes. Let cool completely on wire rack before removing from baking pan, about 1 hour.
Transfer green layer onto a baking sheet. Spread apricot preserves evenly over green layer. Carefully place uncolored layer on top. Spread raspberry preserves evenly over uncolored layer. Top with red layer.
Microwave chocolate in small microwave-safe glass bowl on high for 1 minute, stirring every 30 seconds, until melted. Spread half the melted chocolate evenly over the red layer. Refrigerate until chocolate is set, about 15 minutes.
Microwave chocolate again on high for 1 minute, stirring every 30 seconds until melted. Flip cake over, chocolate-side-down, and spread the remaining melted chocolate evenly over the green layer. Refrigerate again until chocolate is set, about 15 minutes. Slice into 36 rectangles. Store in an airtight container at room temperature until ready to serve.
Tip: If your almond paste is too hard, simply microwave on high for 30 seconds until softened.