Spray a nonstick skillet with cooking spray and heat over medium-low. Place 2 tablespoons of Parmesan cheese at a time into the skillet, cook until cheese melts into circles, bubbles, and browns at the edges, about 1 minute. Flip and cook the other side for 30 seconds. Cool on a plate. Repeat 3 more times.

Heat 1 teaspoon of olive oil in a skillet over medium heat. Add pine nuts and stir until lightly toasted and aromatic, about 3 minutes. Remove from skillet and set aside.

Cook gnocchi according to package directions. Drain in a colander.

Pour 1 tablespoon of olive oil in a large skillet over high heat. Add zucchini, cook and stir for 2 minutes, until seared. Remove from pan. Lower heat to medium, add mushrooms, and stir until they begin to release juices but remain firm, about 5 minutes. Drain juices, return zucchini, and add tomatoes, basil leaves, toasted pine nuts, gnocchi, and remaining olive oil. Cook and toss together until heated through.