Preheat oven to 400˚F.
In a mixing bowl combine tomatoes, garlic cloves, oil, tomato paste, oregano, and thyme. Season with salt and pepper and toss together.
Transfer mixture to a parchment lined baking sheet and roast for 35 to 40 minutes or until the tomatoes just begin to char and have cooked down a bit.
Remove from oven and allow tomatoes to cool for about 20 minutes.
While the tomatoes cool, fill a large pot with water and bring to a boil over med-high heat. Add a small handful of salt, the pasta and boil for 7 to 9 minutes or until cooked to desired doneness. Drain and set aside.
Remove peels from garlic cloves and transfer tomato mixture (including peeled cloves) to a food processor with the butter, lemon zest, and a few grinds of pepper. Blend mixture until fully combined and smooth. Add salt as needed and pulse to combine.
Pat shrimp dry and season with salt and pepper. Place a large skillet over medium-high heat and add 2 1/2 tablespoons butter. Add the shrimp and sear on each side, 2 to 3 minutes.
Add 2 to 3 tablespoons of water to the skillet and immediately cover with a lid (to steam and finish cooking the shrimp through).
After 1 to 2 minutes remove lid and transfer shrimp to a plate.
Wipe skillet clean with a paper towel and add 6 tablespoons of the tomato butter.
Once butter has melted add pasta. Toss together until fully coated.
Add shrimp, Parmesan, and basil into skillet and toss together until evenly coated. Adjust seasonings as needed.
Top pasta with more grated parmesan and basil leaves and serve.