Heat extra virgin olive oil in a large skillet over medium-high heat. Add gnocchi then spread in one layer and saute undisturbed for 3-4 minutes, or until golden brown on the bottom. Toss then continue sauteing for 3-4 more minutes or until golden brown on all sides. Remove skillet from heat then set aside.
Meanwhile, heat butter in another large skillet then add zucchini, corn, and onion, and then season with salt and pepper. Saute until vegetables are tender, about 3-4 minutes, then add chopped garlic and half the basil, and then saute for 30 more seconds. Remove skillet from heat then add half & half and parmesan cheese, and stir to combine. Pour mixture into skillet with gnocchi then toss to combine. Season with more salt and pepper if necessary then serve topped with remaining chopped basil.