Preheat the oven to 375ºF.
In a large bowl mix the butter and sugar. Add the eggs and stir until well mixed.
Add the cornmeal, ¼ cup of all purpose flour and stir just until the dough comes together. Knead the dough a few times in the bowl.
Turn out the dough onto a lightly floured work surface. In a small bowl mix the rest of the flour with the cheese.
Divide the dough into 20 equal pieces and make small bowls.
Working with one piece at a time, gently spread the dough,leaving at least ½ inch of uncovered area around the edges.Take about 2 tablespoons of the cheese mixture and place on top.
Fold the edges up over the filling, overlapping them in soft folds (leave part of the center of the cheese filling uncovered).Place on the baking sheet and continue with the remaining dough.
Bake for about 30 minutes, or until golden. Serve warm.