Bring a large pot of salted water to a boil. Cook the ditalini until al dente according to package directions. Reserve 1 cup of pasta water, then drain.
Heat a large skillet over medium heat. Add the olive oil and garlic, and sauté for about 30 seconds until fragrant.
Add the cherry tomatoes and a pinch of salt. Toss and cook for 4-6 minutes, until they soften and begin to break down.
Pour in the white wine. Let it simmer until most of the liquid has evaporated, about 2-3 minutes.
Stir in the tomato paste and let it cook for 1 minute to caramelize slightly.
Pour in the heavy cream, add ¼ cup of the Parmesan, chili flakes, and black pepper. Lower the heat to medium-low and simmer for 2-3 minutes.
Add the cooked ditalini to the skillet along with another ¼ cup of Parmesan. Add about 6 tablespoons of pasta water to help emulsify. Stir continuously until the sauce thickens and coats the pasta. Add extra pasta water as needed until creamy and glossy.
Turn off the heat and stir in the fresh basil. Taste and adjust salt.
Spoon the pasta into bowls. Top with chopped parsley, torn burrata, extra chili flakes, a drizzle of olive oil, and more Parmesan.
