Preheat oven to 350 degrees with rack in center. In the bowl of an electric mixer fitted with the paddle attachment, mix together butter and cream cheese. Combine flour, cornmeal, and salt in a small bowl. Add gradually to butter mixture, mixing constantly until well incorporated.
Divide dough into 1-inch balls and press into small muffin tins, using your thumbs to form cups inside the mold. Dough cups should be as even as possible and come up to the top of the tins.
Bake until golden brown, about 20 minutes. Spoon desired filling into cups, and serve.