Dissolve honey and yeast in 1/2 cup warm water in a large bowl; let stand 10 minutes. Add remaining 3/4 cup water and 2 tablespoons oil; stir until blended. Lightly spoon flour into dry measuring cups; level with a knife. Add 2 3/4 cups flour and 1/2 teaspoon salt to yeast mixture; stir until blended. Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining 1/2 cup flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel sticky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.)
Punch dough down. Place dough in a 13 x 9-inch baking pan coated with cooking spray. Pat dough to fit pan. Cover and let rise 30 minutes. Uncover dough. Make indentations in top of dough using the handle of a wooden spoon or fingertips. Cover and let rise 45 minutes or until doubled in size.
Preheat oven to 400°.
Uncover dough. Spoon small dollops of cheese over dough. Gently spread cheese over dough. Sprinkle fig quarters evenly over cheese. Drizzle 1/2 teaspoon oil over dough. Sprinkle with 1/4 teaspoon salt. Bake at 400° for 23 minutes or until browned on bottom and sounds hollow when tapped. Sprinkle with remaining 1/4 teaspoon salt. Serve warm or at room temperature.