Heat extra virgin olive oil in a large skillet over medium-high heat. Add gnocchi then spread in an even layer and saute undisturbed for 3-4 minutes, or until golden brown on the bottoms. Toss then continue to saute for 3-4 more minutes or until gnocchi are golden brown on all sides and tender in the center. Remove skillet from heat then set aside.
Meanwhile, heat butter in another large skillet then add zucchini, corn, and onion, then season with salt and pepper. Saute until vegetables are tender, 3-4 minutes, then add chopped garlic and half the basil and saute for 30 more seconds. Remove skillet from heat then add the 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.