Preheat oven to 325°F. Line baking sheet with parchment paper.
Place tomatoes cut-side up on baking sheet. Drizzle 2 Tbsp olive oil over tomatoes, then sprinkle salt and sugar on top.
Bake tomatoes for 60-75 minutes until tomatoes begin to shrivel and expel juices. Allow tomatoes to cool slightly then transfer to a bowl. Be sure to pour any juices and oil into the bowl, as well.
Add 1/3 cup olive oil, lime zest, lime juice, and balsamic vinegar to bowl. Stir to combine with roasted tomatoes. Season with salt and pepper. Set aside as you cook pasta.
Cook pasta in a large pot of boiling salted water. Cook to al dente according to the pasta's package directions.
Drain pasta and toss with parmesan cheese and chopped basil leaves while pasta is still warm. Then pour in roasted tomatoes with olive oil sauce. Fold until pasta is fully coated with sauce and tomatoes are evenly distributed.