Preheat oven to 375˚F.
Spread butter, garlic and thyme along bottom of a shallow baking dish and top with tomatoes. Season with salt and pepper.
Place tomatoes into the oven and roast for 10 minutes. Remove from oven and fold together until tomatoes are well coated in melted butter. Place tomatoes back into the oven for another 20 minutes or until tomato skins have begun to shrivel and the tomatoes themselves have slightly burst.
While tomatoes roast, fill a large pot with water and bring to a boil.
Add a small handful of salt, followed by the pasta and cook until al dente. Drain into a colander, reserving 1/3 cup of the pasta liquid.
Remove tomatoes from oven and discard thyme sprigs and any tomato stems. Carefully peel garlic and mince. Add garlic back to tomatoes and toss together along with all the juices in the pan.
Place a large skillet over medium-high heat. Add oil and a third of the tomatoes (with the juices).
Add pasta to the skillet and toss together for a few minutes. Season with salt and pepper.
Pour reserved pasta water into the skillet and cook until liquid has evaporated.
Sprinkle Parmesan over pasta and toss together until evenly distributed.
Transfer pasta to a platter and top with remaining tomato mixture (along with juices).
Top with fresh basil leaves and loads more freshly grated Parmesan. Serve.