Bring a large pot of water to a boil. Drop the pasta into the water and cook according to package directions, drain, reserving some of the pasta water. Toss the pasta with a splash of oil and set aside.
Remove the kernels from the corn with a sharp knife.
Melt the butter in a large skillet, add the corn kernels, garlic, and any other optional vegetables. Cook, stirring, until the vegetables are tender, about 6 minutes.
Add the milk, 3 tablespoons of the Parmesan, 3/4 teaspoon salt and 1/2 teaspoon pepper. Bring to a gentle simmer, cook until slightly thickened, about 5 minutes.
Add the cooked pasta, lemon zest and 1/4 teaspoon salt. Gently toss the pasta in the sauce. Sprinkle each serving with the remaining 1 tablespoon Parmesan and some black pepper. Serve with lemon wedges.