1. FOR THE DOUGH: Process whole-wheat flour, bread flour, honey, and yeast in food processor until combined, about 2 seconds. With processor running, add water and process until dough is just combined and no dry flour remains, about 10 seconds. Let dough stand for 10 minutes.

2. Add oil and salt to dough and process until it forms satiny, sticky ball that clears sides of workbowl, 45 to 60 seconds. Remove from bowl and knead on oiled countertop until smooth, about 1 minute. Shape dough into tight ball and place in large, lightly oiled bowl. Cover tightly with plastic wrap and refrigerate for at least 18 hours or up to 2 days.

3. FOR THE PESTO: Process basil, oil, pine nuts, garlic, and 1/2 teaspoon salt in food processor until smooth, scraping down sides of bowl as needed, about 1 minute. Stir in Parmesan and season with salt and pepper to taste. (Pesto can be refrigerated, covered, for up to 2 days.)

4. One hour before baking pizza, adjust oven rack 4 1/2 inches from broiler element, set pizza stone on rack, and heat oven to 500°F. Remove dough from refrigerator and divide in half. Shape each half into smooth, tight ball. Place balls on lightly oiled baking sheet, spacing them at least 3 inches apart. Cover loosely with plastic coated with vegetable oil spray; let stand for 1 hour.

5. Heat broiler for 10 minutes. Meanwhile, coat 1 ball of dough generously with flour and place on well-floured countertop. Using your fingertips, gently flatten into 8-inch disk, leaving 1 inch of outer edge slightly thicker than center. Lift edge of dough and, using back of your hands and knuckles, gently stretch disk into 12-inch-round, working along edges and giving disk quarter turns as you stretch. Transfer dough to well-floured peel and stretch into 13-inch round. Using back of spoon, spread half of pesto in thin layer over surface of dough, leaving 1/4-inch border. Sprinkle with 1/2 cup goat cheese. Slide pizza carefully onto stone and return oven to 500°F. Bake until crust is well browned and cheese is partially browned, 8 to 10 minutes, rotating pizza halfway through baking. Remove pizza, place on wire rack, and let rest for 5 minutes. Slice and serve.

6. Heat broiler for 10 minutes. Repeat process of stretching, topping, and baking with remaining dough and toppings, returning oven to 500°F when pizza is placed on stone.

Makes two 13-inch pizzas