Heat oven to 375°F. Unroll dough onto ungreased cookie sheet. Starting at center, press out dough into 15x10-inch rectangle. Bake 10 minutes. Remove from cookie sheet; cool 5 minutes.
Cut cooled crust into 4 rectangles. Top each of 2 rectangles with half of the ham and 4 triangles of cheese. Cover each with remaining crust rectangle.
Meanwhile, heat 12-inch skillet or cast iron skillet over medium-high heat. Spray outsides of each sandwich with cooking spray. Place 1 sandwich in skillet. Place smaller skillet on sandwich to flatten slightly. Cook 1 to 2 minutes, turning once, until crisp and thoroughly heated. Repeat with remaining sandwich. Cut each sandwich into quarters.