In a standing mixer fitted with a paddle, or in a bowl using a hand-held beater, cream the butter, cream cheese, and sugar until well blended. Add the egg and mix until incorporated. Add the flour and mix until incorporated.
Wrap the dough in plastic wrap and chill overnight.
On a work surface sprinkled with confectioner's sugar, divide the dough into 4 equal pieces. Working in 4 batches, roll the dough out to 1/4-inch thick. Using a 2 1/2-inch biscuit cutter, cut out small rounds and transfer them to a parchment-lined cookie sheet.
Using your thumb, make a slight indentation in each cookie. Fill each indentation with the filling of your choice.
Chill the cookies while you preheat the oven to 375 degrees F.
Bake the cookies until lightly browned, about 15 to 17 minutes.