Grilled Pizza with Eggplant and Tomatoes

Name: Grilled Pizza with Eggplant and Tomatoes
Ingredients: 1/4 cup (2 fl. oz./60 ml) extra-virgin olive oil, plus more as needed; 1/4 cup (2 fl. oz./60 ml) balsamic vinegar; Coarse kosher salt and freshly ground pepper, to taste; 2 Asian eggplants, about 1/2 lb. (250 g) total weight, cut lengthwise into 1/3-inch (9-mm) slices; 1 small red onion, cut crosswise into 1/3-inch (9-mm) slices; 1 lb. (500 g) purchased fresh pizza dough; 1/2 lb. (250 g) fresh whole-milk mozzarella cheese, shredded; 1 cup (6 oz./185 g) small cherry tomatoes, halved crosswise; 1/2 cup (2 oz./60 g) grated pecorino romano cheese; 1/2 tsp. red pepper flakes; 3 Tbs. slivered fresh basil; 2 Tbs. minced fresh marjoram