Generously season the chicken with salt and pepper.
Add the olive oil to a heavy bottomed pot (dutch oven) and heat over medium-high heat. Once the oil is hot, add the chicken strips and cook until lightly browned all over, 2-3 minutes. Remove chicken to separate plate to rest, set aside.
Add the butter to the pot and sauté the onion and garlic for 1-2 minutes until translucent. Add in the oregano and chili flakes, sauté 1 more minute.
Add in the tomato paste and stir while cooking for 1-2 minutes until it evenly coats the onion and garlic. Add the white wine and cook while stirring for 1-2 minutes. Add the cherry tomatoes and cook for 1 more minute.
Stir in the chicken broth, heavy cream, and dry pasta. Return the chicken to the pot and bring the mixture to a simmer.
Once simmering, turn the mixture down low and let simmer for 14-15 minutes, until the pasta is cooked through, stirring every 2 minutes. This keeps the pasta from sticking together and getting gummy-like.
Once the pasta is cooked, turn off the heat and stir in the parmesan cheese. Remove the the burrata balls from the water and set on a small plate. One at a time, using your hands, tear the buratta into pieces over the top of the pasta. Cover the pot with a tight fitting lid and let sit for 5 minutes until it gets melty.
Remove the lid and sprinkle the fresh basil on top. You can either stir the burrata to mix it in, or serve as is with it melted on just the top.