Bring a large pot of heavily salted water to a boil. Do not add the angel hair yet -- it cooks in under 2 minutes and should go in late.

Warm the olive oil in a large skillet over medium heat. Add the garlic and cook until fragrant, about 1 minute. Add the tomatoes, salt, and pepper. Cook, stirring occasionally, until the tomatoes are softened and beginning to burst, about 5-7 minutes.

Drop the angel hair into the boiling water. After about 1 minute, use a ladle to scoop out approximately 1/2 cup of pasta water and add it directly to the tomato mixture. Using a spoon or spatula, mash the tomatoes into the liquid to form a loose sauce.

Add the butter to the sauce a piece at a time, stirring until fully melted and emulsified.

Using tongs, transfer the pasta directly from the pot into the skillet (a minute of cook time is ideal -- it will finish in the sauce). Add the basil and toss until the pasta is evenly coated. Add a splash more pasta water if the sauce needs loosening.

Divide into bowls and top each portion with a generous dollop of burrata. Finish with fresh basil, cracked black pepper, and a drizzle of olive oil.