Preheat oven to 450°F.
In a medium bowl, mix together ¼ cup olive oil, 1 tbsp sun-dried tomato spread, minced garlic, thyme, oregano, red pepper flakes, salt, and black pepper.
Place grape tomatoes and sliced shallots in a large baking dish. Pour the seasoned olive oil mixture over top and toss to coat.
Dot the top evenly with the 3 tbsp butter.
Bake for 20–25 minutes, until tomatoes are blistered, jammy, and lightly caramelized.
While veggies bake, cook fusilli pasta in a large pot of salted boiling water until al dente.
Reserve ½–¾ cup pasta water, then drain.
When tomatoes are done, remove dish from oven.
Stir gently, smashing some of the tomatoes to release their juices.
Add in the hot cooked pasta and ¼ cup reserved pasta water, tossing until everything is coated in the saucy roasted mixture. (Add more pasta water as needed for desired sauce consistency.)
Nestle the burrata right on top of the hot pasta.
Cover the baking dish loosely with foil for 2–3 minutes to gently warm the burrata.
Remove foil, scatter with chopped fresh parsley (or basil), and break open the burrata so the creamy center melts into the pasta.
Optional: finish with a grate of lemon zest or squeeze of lemon juice for extra brightness.