Bring a large pot of salted water to a rolling boil. Add the uncooked pasta and cook according to package instructions, usually about 8-10 minutes, until al dente. Reserve about 1/4 cup of the pasta cooking water before draining the pasta and set it aside.

In a large skillet, heat 1 tablespoon of olive oil over medium heat. Once shimmering, add the finely chopped shallot. Sauté for about 2 minutes, stirring occasionally, until the shallot turns translucent.

Stir in 1/4 teaspoon of chili flakes and 2 tablespoons of tomato paste into the skillet. Cook for another minute, stirring well to combine, allowing the paste to caramelize slightly.

Add in 8-10 halved grape tomatoes, tossing them gently in the spicy mixture. Cook for 3-4 minutes, stirring occasionally until the tomatoes soften and begin to burst.

Pour in 1/4 cup of heavy cream into the skillet and stir to combine. Allow the mixture to simmer for 1-2 minutes, adjusting seasoning with 1/4 teaspoon of kosher salt and 1/8 teaspoon of black pepper.

Carefully add the drained pasta to the skillet, tossing it well with the sauce to ensure it's evenly coated. Use reserved pasta water to adjust the sauce's thickness if necessary.

Remove the skillet from heat and stir in 1-2 tablespoons of freshly chopped basil. Place the fresh burrata on top of the pasta, cutting it open to allow the creamy center to spill into the rigatoni.