To prepare flatbreads, lightly spoon whole wheat flour into a dry measuring cup; level with a knife. Combine whole wheat flour, 1/4 cup water, and yeast in a bowl; let stand 10 minutes.
Lightly spoon all-purpose flour into dry measuring cups, and level with a knife. Combine 2 cups all-purpose flour, 1/2 teaspoon salt, and remaining 3/4 cup water in a large bowl. Add yeast mixture, and stir until a dough forms. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining 1/4 cup all-purpose 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.)
Preheat oven to 450°.
Punch dough down; cover and let rest 5 minutes. Divide dough in half. Roll each half into a 9-inch circle on a lightly floured surface; place on baking sheets sprinkled with cornmeal. Lightly coat dough with cooking spray. Sprinkle dough evenly with sliced garlic; press garlic into dough using fingertips. Bake at 450° for 10 minutes or until crisp and garlic begins to brown. Remove flatbreads from oven; cool on wire racks.
To prepare topping, combine vinegar, oil, 1/4 teaspoon salt, pepper, and minced garlic in a medium bowl. Add tomatoes; toss gently.
Sprinkle each flatbread with 1/2 cup cheese; broil flatbreads 1 minute or until cheese melts. Remove from oven; top each flatbread with half of tomato mixture. Sprinkle each flatbread with 1/4 cup basil. Cut each flatbread into 6 equal wedges.