Beat egg yolks and almond paste together in a bowl using a mixer on medium speed until crumbly, about 2 minutes. Add butter, sugar, and salt to almond paste mixture and beat until creamy, about 3 minutes; reduce speed to low and gradually beat in flour just until blended.
Divide dough into 4 pieces and flatten each into a disk on a lightly floured surface. Wrap each disk in plastic wrap and chill for 2 hours.
Preheat oven to 375 degrees F (190 degrees C).
Place 1 dough piece on a lightly floured surface and roll into 1/4-inch thickness using a floured rolling pin. Cut dough into shapes using floured cookie cutters. Arrange cookies 1-inch apart on a large baking sheet. Form any remaining scraps into a disk and refrigerate.
Bake in the preheated oven until lightly browned, 10 to 12 minutes. Transfer cookies to a wire rack to cool. Repeat with remaining dough.