Preheat the oven to 400F and line a rimmed baking sheet with parchment paper or aluminum foil.
Add the tomatoes, 1 tablespoon olive oil, 1 minced garlic clove, and minced thyme to the baking sheet. Season with salt and pepper to taste. Toss to combine.
Bake the tomatoes for 15-18 minutes, or just until they begin to burst.
While the tomatoes roast, cook the pasta to al dente in salted boiling water according to the time on the package. When the pasta is al dente, remove ? cup of the starchy pasta water and then drain the remaining water and set the pasta aside.
In a large skillet set over medium heat, add the remaining tablespoon of olive oil and the remaining minced clove of garlic. Cook for 1-2 minutes, or just until the garlic is fragrant.
Add the butter, lemon juice, and red pepper flakes. Once the butter has melted, add the reserved pasta water and stir to combine. Cook for 2-3 minutes, or until the sauce has thickened slightly.
Add the pasta to the sauce and toss to combine. Season with salt and pepper to taste.
Add the tomatoes on top of the pasta and crumble over the goat cheese. Garnish with fresh basil and enjoy.
Store any leftover pasta in an airtight container in the fridge for up to three days.