Beat together sugar, butter, cream cheese, egg yolk, salt, almond extract, and vanilla in a large bowl with an electric mixer until smooth. Gradually mix in flour until dough comes together.
Divide dough into thirds and form each piece into a disk. Wrap tightly with plastic wrap and refrigerate, 8 hours to overnight.
When ready to bake, preheat the oven to 375 degrees F (190 degrees C).
Working with one disk at a time, roll dough on a lightly floured surface to an 1/8-inch thickness; keep other disks refrigerated until ready to roll. Cut dough into desired shapes with lightly floured cookie cutters. Place cookies 1 inch apart onto ungreased baking sheets.
Bake in the preheated oven until cookies are light golden brown, 7 to 10 minutes, switching racks halfway through. Remove from the oven and transfer cookies to wire racks.