Preheat the oven to 325 degrees F and line a 10x15-inch pan with parchment.
In a large, very clean mixing bowl with a very clean whisk attachment, whip the egg whites until foamy.
Add ¼ cup of the sugar into the whites very slowly, while continuing to whip.
When all the sugar has been added, turn the mixer up to high speed and whip until the meringue can hold a stiff peak.
Transfer the meringue to a separate bowl, then beat the almond paste, butter, almond extract, and remaining ¾ cup of sugar together with the paddle attachment until smooth and fluffy.
Beat in the egg yolks until combined.
Mix in the flour and salt until combined, then fold in the meringue in 2 or 3 additions by hand with a silicone spatula.
Divide the batter into 3 equal portions (approx. 13.6 ounces each), tinting one with red food coloring, one with green food coloring, and leaving the third white.
Carefully transfer the batters to the prepared pan, spreading them into an even layer but keeping the colors separate from one another.
Bake until set (approx. 10 to 12 minutes).*
Cool completely, then lift out of the pan and cut the different colors apart along their borders.
Spread half the jam over the green layer, then stack the white layer on top.
Spread the remaining jam over the white layer, then stack the red layer on top.
Place another sheet pan on top of the layered cake and weigh it down with a skillet or cans, then refrigerate overnight.
Warm the cream gently (in a small pot on the stove over low heat, or in a glass measuring cup in the microwave) until steamy.
Place the chocolate and corn syrup in a medium bowl, and pour the hot cream on top.
Allow the hot cream/chocolate mixture to stand for about 5 minutes.
Add the vanilla and whisk the mixture until smooth.
Pour the warm chocolate glaze over the cake, using a spatula to spread it out and over the edges.
Refrigerate to set the chocolate glaze, then trim away the outside edges.
Use a sharp knife to cut 1 ¼- by 1 ¼-inch squares, rinsing the blade with hot water and drying it after each cut.