Preheat an oven to 400ºF. Bring a large pot of water to a boil over high heat. Generously salt the water, add the pasta and cook, stirring occasionally, until al dente, about 8 minutes. Drain the pasta and rinse under cold running water. Set aside.
In a 12-inch nonstick fry pan over medium-high heat, warm 3 Tbsp. of the olive oil. Add the corn, season with salt and black pepper and cook, stirring occasionally, until the corn is lightly golden, 6 to 8 minutes. Transfer to a large bowl. Set aside.
Return the pan to medium-high heat and warm the remaining 3 Tbsp. olive oil. Working in batches, add the zucchini, season with salt and cook, stirring occasionally, until the zucchini is tender and golden brown, 6 to 8 minutes. Add to the bowl with the corn. Repeat with the remaining zucchini, adding more oil to the pan as needed.
Set the pan over medium-low heat. Add the onion, 1 tsp. salt and black pepper, to taste. Cook, stirring occasionally, until the onion is translucent, about 2 minutes. Stir in the tomatoes, garlic, oregano and red pepper flakes and cook, stirring occasionally, until the tomatoes soften and begin to form a sauce, about 5 minutes. Stir in the tomato paste and cook for 1 minute. Add the wine and cook until the wine has reduced and the sauce is fairly thick, about 3 minutes more.
Add the pasta, tomato sauce, basil, mozzarella and half of the Parmigiano-Reggiano to the bowl with the vegetables and stir to combine.
Transfer to the fry pan and sprinkle the remaining Parmigiano-Reggiano on top. Transfer the pan to the oven and bake until golden brown on top, 20 to 25 minutes. Serve warm.