Boil the pasta water and salt it. Season the chicken with salt and pepper. In a large pan, heat 2 tbsp olive oil and 1 tbsp butter on medium-high heat. Add the chicken and cook 3-4 minutes per side, or until cooked through (165°F). Remove and set aside.
In the same pan, lower heat to medium. Add the onion, garlic and red pepper flakes. Cook 2-3 minutes.
Add the tomato paste and cook 1-2 minutes. Add the cherry tomatoes and cook 5-7 minutes, until they start to soften.
In the meantime, add the pasta to the boiling salted water and cook until al dente.
Add the heavy cream, chicken broth and parmigiano cheese. Keep on medium and allow to slow bubble, cooking down until the pasta is done, stirring occasionally.
Add a ladle of pasta water, the cooked pasta, basil, 1 tbsp butter, salt and pepper.
Top with the cooked chicken and torn burrata, drizzle with olive oil and enjoy!