How to Make It
Beat flour, 1/2 cup water, 1/4 cup oil, and 1 teaspoon salt with a stand mixer fitted with the dough hook attachment on medium-low speed until dough is soft and slightly sticky, 4 to 5 minutes. Turn dough out onto a floured surface; knead until smooth and elastic, about 8 minutes, dusting lightly with flour as needed. Wrap dough ball tightly in plastic wrap; let rest at room temperature 3 hours.
Place a pizza stone on middle rack of oven. Preheat oven to 500°F. Brush a 15-inch round rimmed baking pan (such as a copper focaccia pan) with 1 tablespoon oil. Unwrap dough ball; divide in half. Roll each half into a 16-inch circle on a lightly floured surface, picking up and carefully stretching dough as needed. Stretch 1 dough round over prepared pan, allowing a 1/2-inch overhang around pan lip. Dot cheese evenly over dough; top with second dough round, allowing a 1/2-inch overhang around pan lip. Gently press overhanging dough around pan lip to seal. Trim off excess dough; discard. Tear 6 to 8 small holes in top dough layer (to allow steam to escape). Brush dough with remaining 2 tablespoons oil, and sprinkle with remaining 1/4 teaspoon salt.
Place pan on preheated pizza stone; bake in preheated oven until focaccia is golden brown and bubbly, 12 to 14 minutes. Cut into squares, and serve immediately.