1. FOR THE CRUST: Combine oil and water in liquid measuring cup. In food processor fitted with plastic dough blade or metal blade, process bread flour, whole-wheat flour, sugar, salt, and yeast until combined, about 5 seconds. With machine running, slowly add liquid through feed tube; continue to process until dough forms tacky, elastic ball that clears sides of workbowl, about 1 1/2 minutes. If dough ball does not form, add more flour 1 tablespoon at a time and process until dough ball forms. Spray medium bowl lightly with nonstick cooking spray or rub lightly with oil. Transfer dough to bowl and press down to flatten surface; cover tightly with plastic wrap and set in draft-free spot until doubled in volume, 1 1/2 to 2 hours.

2. When dough has doubled, press down gently to deflate; turn dough out onto work surface and divide into 4 equal-sized pieces. With cupped palm, form each piece into smooth, tight ball. Set dough balls on well-floured work surface. Press dough rounds with hand to flatten; cover loosely with plastic wrap and let rest about 15 minutes.

3. FOR THE TOPPING: Meanwhile, toss tomatoes and table salt in medium bowl; transfer to colander and drain 30 minutes (wipe out and reserve bowl). Shake colander to drain off excess liquid; transfer tomatoes to now-empty bowl and set aside. Combine cheeses in second medium bowl and set aside.

4. Gently stretch dough rounds into disks about 1/2-inch-thick and 5 to 6 inches in diameter. Working one piece at a time and keeping the rest covered, roll out each disk to 1/8-inch thickness, 9 to 10 inches in diameter, on well-floured sheet of parchment paper, dusting with additional flour as needed to prevent sticking. (If dough shrinks when rolled out, cover with plastic wrap and let rest until relaxed, 10 to 15 minutes.) Dust surface of rolled dough with flour and set aside. Repeat with remaining dough, stacking sheets of rolled dough on top of each other (with parchment in between) and covering stack with plastic wrap; set aside until grill pan is ready.

5. TO PAN-GRILL AND BAKE: Adjust oven racks to upper-middle and lower-middle positions and heat oven to 400°F. Set two wire racks into rimmed baking sheets and set aside. Lightly flour pizza peel (or rimless baking sheet); invert one dough round onto peel, gently stretching it as needed to retain shape (do not stretch dough too thin; thin spots will burn quickly). Brush grill pan with oil and heat over medium-high until barely smoking, 2 to 3 minutes. Peel off and discard parchment; carefully slide round onto grill pan. Cook 1 to 1 1/2 minutes until clear grill marks form on underside of dough (use tongs to check), then rotate dough 90 degrees piercing large air bubbles with paring knife, and cook for an additional minute. Lower heat to medium, flip dough, and cook on opposite side for 2 minutes or until spottily charred. Remove to prepared baking sheets (two pizzas per baking sheet) and repeat with remaining dough rounds.

6. Brush all crusts generously with Spicy Garlic Oil; top each evenly with one-quarter of cheese mixture and one-quarter of tomatoes. Place baking sheets in oven and bake until cheese, melts about 6 to 8 minutes, rotating the pans halfway through cooking. Transfer pizzas to cutting board and sprinkle with basil and coarse salt to taste; cut into wedges and serve immediately.

Makes four 9-inch pizzas