Heat the oven to 425°F and line an 18-by-13-inch rimmed sheet pan with parchment rated for that temperature. Toss gnocchi, tomatoes and zucchini with olive oil, garlic, salt and pepper directly on the pan.
Spread in one layer with some bare space between the pieces and roast for 15 minutes.
Turn the gnocchi and vegetables and roast for 10 to 12 minutes more until gnocchi edges brown and tomatoes split.
Scatter mozzarella in small pieces across the tray and return to the oven for 2 to 3 minutes just until the cheese softens.
Drizzle with balsamic vinegar and fold in torn basil. Divide among 4 bowls while the gnocchi edges still have some chew.