Add the cookie dough, almond paste, preserves, and flour to the bowl of a mixer.
Mix until everything is combined. (Or you can do this by hand, just knead it together.)
Pat the dough into a rectangle, about 6x9. Cut into 24 pieces.
Whisk the egg whites in a small bowl. Put the almonds on a plate.
Roll the dough into balls. Flatten into 3-inch disks.
Brush the tops with egg whites. Sprinkle generously with almonds.
Bake in a preheated 375 oven for 13 to 18 minutes. Cool on the sheet for two minutes, then cool completely on a rack.