Heat oven to 400°.
Cut butter into flour until you get grains the size of peas. Add sugar and ¼ cup ice water and mix until you form a smooth dough. On a floured surface, roll dough in a 12-inch circle and transfer it to a baking sheet.
Sprinkle cheese around the center of the dough, leaving a 2-inch border all the way around. Layer the apples artistically to cover the cheese. Fold the edges of the dough up over the apples, leaving the center open.
Bake until the apples are soft and the dough is lightly browned, about 35 minutes.