Cook the pasta in a large pot of salted boiling water according to package directions until al dente, about 4-5 minutes. Reserve 1 cup of pasta water before draining.
In a skillet, heat extra virgin olive oil over medium heat. Add the cooked pasta and reserved pasta water, stirring to combine.
Stir in the Parmesan cheese, salt, pepper, and chili flakes, mixing until creamy.
Top the pasta with torn pieces of burrata cheese and chopped basil before serving.
Serve immediately, garnished with extra basil and a drizzle of olive oil if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 2 days.