Heat oven to 400 degrees. Line a baking sheet with parchment or foil. Add the tomatoes and olive oil and toss to coat. Season with salt and pepper, then add the leaves from one sprig of thyme and roast for about 20 minutes, or until the tomatoes burst and pucker.

Meanwhile, bring a large pot of water to a boil. Season with salt and cook the pasta until al dente. Drain, reserving 1 cup of the pasta water. Set aside.

In the now empty pot, melt the butter over medium-low heat. Add the garlic and a pinch of salt. Cook for about 1 minute, until fragrant. Scrape in the tomatoes and their juices. Add the cream and remaining thyme, stirring to combine. Bring to a simmer over low heat and cook until the cream has slightly thickened.

Remove from heat. Stir in the parmesan and basil. Add water if needed to loosen the sauce. Return the pasta to the pot and toss with the sauce. Season with additional salt and pepper, if needed, and serve immediately, topping with extra parmesan.