Bring a large pot of salted water to a boil. Add pasta shells and cook according to package directions.
Heat 1 tbsp olive oil over medium-high heat in a large skillet. Add tomatoes and minced garlic, then stir gently to combine. Cook until tomatoes are lightly blistered, about 2 to 3 minutes, shaking the pan occasionally.
Add the white wine, lower heat to a simmer and scrape the bottom of the pan with a wooden spatula to release the garlic.
Stir in fresh chopped basil and sea salt. Simmer for another 2 to 3 minutes.
Add 1/2 tsp of the extra virgin olive oil and 1 tsp balsamic vinegar. Stir gently to combine and remove from heat.
Drain the cooked pasta and toss with 1 tbsp of the extra virgin olive oil. Then, transfer the cooked pasta to the skillet and stir to combine.
Spoon cooked pasta with tomatoes and sauce onto two plates. Top each plate with about 2 oz fresh burrata cheese, a generous drizzle of balsamic vinegar, and fresh basil leaves.
Serve immediately with a side of fresh bread and a glass of wine.