Dissolve yeast in warm water. Combine 2 tablespoons oil, honey, salt, yeast mixture and 1-1/2 cups flour; beat on medium speed until smooth. Stir in enough remaining flour to form a soft dough (dough will be sticky).
Turn dough onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease the top. Cover; let rise in a warm place until doubled, about 1 hour.
Punch down dough; divide into 6 portions. On a lightly floured surface, roll each portion into an 8x6-in. rectangle. Place each on a greased piece of foil. Spritz with cooking spray; cover and let rest 10 minutes.
In batches, carefully invert crusts onto greased grill rack; peel off foil. Grill, covered, over medium heat until bottom is golden brown, 2-3 minutes. Turn; grill until bottom begins to brown, 1-2 minutes.
Remove from grill. Brush tops with remaining oil; top with tomatoes. Grill, covered, until bottom is golden brown and tomatoes are heated through, 1-2 minutes. To serve, add basil, drizzle with glaze and, if desired, top with cheese.