How to Make It
Beat flour, water, salt, and 1/4 cup of the oil with a stand mixer fitted with a 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 450ºF. Brush a 15-inch round rimmed baking pan (such as a pizza pan) with 2 tablespoons of the oil. Unwrap dough ball; divide in half. Roll each half into a 16-inch round 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. Sprinkle cheese evenly over dough. Top with second dough round, allowing a 1/2-inch overhang around pan lip. Gently press top and bottom dough overhangs together around pan lip to seal. Fold overhanging dough up and in toward center of pan, gently crimping with fingers to create a thin crust around pan edge. Cut 6 small slits in top dough layer (to allow steam to escape while baking). Brush dough with remaining 2 tablespoons oil.
Place pan on preheated pizza stone; bake at 450°F until focaccia is golden brown and bubbly, 15 to 18 minutes. Serve immediately.