Butternut Squash Gnocchi Cacio e Pepe

Ingredients

• 2, lb. ,Talluto's Butternut Squash Gnocchi
• 1, small ,zucchini, thinly sliced
• 1, small ,yellow squash, thinly sliced
• 1, stick ,salted butter
• 1/2, cup ,light flavored oil, for frying
• 4, oz. ,Fleshly grated Pecorino Romano cheese
• 4, oz. ,Freshly grated Parmigiano cheese
• 1/2, tsp. ,Kosher salt
• 1, tsp. ,Coarsly ground black pepper
• 2, oz. ,pasta water