Bring large pot of water to boiling. Heat charcoal grill or gas grill to medium-hot (or use cast-iron skillet).
Stem, rinse and chop spinach. Transfer to large salad bowl with mozzarella, olives and basil.
Add pasta to boiling water; cook for 11 minutes or until tender.
Whisk vinegar, lemon juice, sugar, salt, black pepper and oil in small bowl.
Once grill is hot, cut tomatoes into 1/2- to 3/4-inch-thick slices. Dip tomato slices into dressing. Grill 8 to 10 minutes, turning once. Reduce cooking time if tomatoes become too soft. OR: If not using grill, heat cast-iron skillet over medium heat. Cook slices 2 minutes, turning once.
Drain pasta; add to spinach mixture in bowl. Toss with dressing and grilled tomatoes. Serve slightly warm.