Line 2 quarter sheet pans (each 12 inches by 9 inches) with unbleached parchment paper, and set them aside.
In the bowl of a stand mixer fitted with the paddle attachment or a large bowl with a hand mixer, place the almond paste and butter and beat until well-combined and creamy.
Add the sugar, salt and eggs, beating to combine well after each addition. The batter should be thick.
Add the flour and xanthan gum, and mix until the dough is smooth.
Divide into 2 equal parts and spread into an even layer in each prepared pan, using a wet spatula.
The dough will be sticky.
Place each pan, one at a time, in the center of the preheated oven and bake for 12 minutes, or until the cake just begins to brown around the edges.
Remove the pan from the oven and allow to cool slightly.
Invert one cake onto a large piece of parchment paper on top of a cutting board, and evenly spread the jam on it.
Invert the second layer carefully on top, taking care not to handle the cakes too much or they’ll begin to crack.
If the cake cracks, just press it together as the jam will hold it firmly in place.
Place a sheet of parchment paper on top. If the top cake has cracked at all, invert the entire stack so that the cracked cake is on the bottom.
Place a heavy book or other flat object on top of both cakes to compress the layers.
Place the stack of cakes, along with the book perched on top, in the refrigerator for about 30 minutes, or until the layers are compressed.
Remove from the refrigerator, remove the top sheet of paper, and cut the compressed cake into 1 1/2-inch squares with a sharp knife or square cookie cutter.
Place the square cakes on a wire rack over a parchment-lined sheet pan, and set aside.
Make the icing
Place the confectioners’ sugar and meringue powder in a medium-sized bowl and whisk to combine.
Add 2 tablespoons of the milk and mix to combine.
It should form a thick paste. Add more milk by the quarter-teaspoonful, mixing vigorously until it reaches a very thickly pourable consistency.
Spoon the icing over the individual cakes.
For extra fancy petit fours, add a drop or two of gel food coloring to some of the icing, and drizzle over the top of the white icing. Allow to set at room temperature