Preheat oven to 425°F.
While the oven is preheating, bring a large pot of salted water to a boil over high heat. Gather all ingredients.
Put cherry tomatoes in a 13-by-9-inch baking dish. Drizzle them with 3 tablespoons of olive oil. Sprinkle with lack pepper and 1 teaspoon of salt. Toss to coat. Push the tomatoes to the outer edges of the dish, and place the garlic and herb cheese in the center. Drizzle the cheese with the remaining 1 tablespoon of olive oil.
Bake in the oven until the tomatoes are blistered and the cheese has softened for 25 to 30 minutes.
Meanwhile, add the pasta to the boiling water and cook until al dente, about 9-11 minutes.
Drain, reserving ¾-1 cup of the pasta cooking water.
Remove the baking dish from the oven and add ¼ cup of the pasta water; stir until creamy.
Add the pasta and stir until well-coated. Stir in Parmesan, the remaining ½ teaspoon salt, and up to ½ cup more pasta water, 2 tablespoons at a time, to reach the desired consistency.
Garnish with basil and black pepper, and serve immediately.