Heat the extra virgin olive oil in a large, nonstick skillet over medium-high heat. Add the gnocchi then spread into an even layer and let sit undisturbed until the bottoms are golden brown, 3-4 minutes. Stir the gnocchi then continue to saute for 3-4 more minutes, stirring frequently, until the gnocchi are golden brown all over and tender in the centers. Transfer the gnocchi to a plate then set it aside.
Melt the butter in the skillet still over medium-high heat. Add the zucchini, sweet corn, and onions, season with salt and pepper, then saute until the zucchini is crisp-tender, 4-5 minutes – don overcook the zucchini. Add the cherry tomatoes, garlic, and basil then saute until the cherry tomatoes begin to burst, 2 minutes.
Add the half & half then stir to combine. Once the half & half starts bubbling around the edges of the skillet, turn the heat down to medium, sprinkle in the parmesan cheese, then stir to combine. Add the crispy gnocchi then stir to combine and simmer until the gnocchi are heated through and the sauce has slightly thickened, 1-2 minutes.
Remove the skillet from the heat then let it sit for 5 minutes to thicken. Taste and adjust salt and pepper if necessary then scoop into bowls and serve.