1. Preheat grill to medium-high heat (350° to 400°). Slice zucchini and yellow squash lengthwise into 6 slices. Brush with 1 1/2 tablespoons oil, and sprinkle with salt. Grill 2 minutes on each side or until tender. Dip in Peanut-Ginger Sauce to coat; set aside squash and remaining sauce.
2. Shape dough into 2 (9- to 9 1/2-inch round) crusts. Brush both sides with remaining 2 teaspoons olive oil. Grill 3 to 5 minutes; flip crusts, and top with 1 cup mozzarella cheese, reserved grilled squash and zucchini, and remaining 1 cup cheese. Grill, covered with grill lid, 4 minutes or until crust is cooked through and cheese melts.
3. Place pizzas on a cutting board, and top with green onions and next 4 ingredients. Drizzle with remaining Peanut-Ginger Sauce. Serve immediately.