Preheat oven to 325ºF (160ºC).
To roast vegetables, line a pan with aluminum foil and spread 2 cups cherry tomatoes and 1 cup corn kernels (you can do it separately if you want). Don't mix them; keep them separated, even if using the same pan.
Season with salt and black pepper, and a drizzle of 3-4 tablespoons olive oil.
Roast until tomatoes begin to shrivel and caramelize, and corn is charred in some places, about 30 minutes. The time might vary, depending on your oven.
Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet.
Add 1 shallot, chopped, corn and 1 teaspoon fresh thyme leaves. Cook for a minute or two over medium heat, until the shallot is softened.
Add ½ cup heavy cream and ¼ cup grated parmesan cheese. Season with salt and pepper and stir to combine. Remove from the stove and reserve.
Cook 7 ounces short dried pasta in abundant salted water according to the manufacturer's directions. Drain and transfer to the skillet. Reserve 2-3 tablespoons of the pasta water.
Add the tomatoes, 1 tablespoon chopped fresh basil and ½ tablespoon chopped chives to the pasta. Stir everything together for a minute or two until the pasta is coated. Add some of the reserved pasta water to bind the mixture.
Divide between two serving plates and serve topped with a drizzle of olive oil and ½ tablespoon chopped chives.