Preheat oven to 400 degrees F. In a 3qt baking dish, add olive oil and place goat cheese in the center. Add in tomatoes, garlic, and sliced shallot all around it. Sprinkle with kosher salt and black pepper. Add in 3-4 basil leaves and thyme. Bake for 20-25 minutes until light brown on top and slightly bubbling on the sides. Turn the broiler to high heat and broil for 2-3 minutes until tomatoes are bursting and the cheese turns a golden brown. Watch carefully to prevent burning as broilers vary in heat levels. Remove thyme stems, if using.
Meanwhile, cook pasta according to package directions, drain and set aside, keeping some pasta water behind to refresh the pasta (if it sticks together) and to add to the sauce, if needed.
Mix the pasta into the cheesy tomato sauce till throughly combined. Top with the remaining basil and taste to adjust any seasonings. To thin out the sauce, add 1 tablespoon of pasta water while mixing with the cheese sauce.
Notes
Store up to 3 days in the fridge or freeze after baking.
Mix up the cheese by using Boursin or cream cheese, but the baking time will need to be reduced.
Fresh herbs are optional, but the basil really does add a lovely flavor. I would keep the fresh basil at the very least.