Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente, usually 8-10 minutes. Before draining, reserve 1/2 cup of pasta water, then drain the pasta well and set aside.

Pat the chicken breasts completely dry with paper towels. Season both sides generously with salt and pepper. Heat the olive oil in a large skillet over medium-high heat until shimmering. Add the chicken and sear for 5-7 minutes per side until golden brown and the internal temperature reaches 165°F. Remove chicken to a plate and let rest for 5 minutes.

In the same skillet, reduce heat to medium and add the minced garlic. Sauté for about 1 minute until fragrant but not browned. Pour in the chicken broth and heavy cream, scraping up any browned bits from the bottom of the pan with a wooden spoon.

Stir in the oregano and red pepper flakes if using. Let the sauce simmer gently for 3-4 minutes until it coats the back of a spoon. Remove from heat, add the Parmesan cheese, and whisk until melted and smooth.

Slice the rested chicken into strips and return it to the skillet along with any accumulated juices. Return to low heat, add the drained pasta, and toss everything together until the pasta is completely coated in the creamy sauce. If the sauce seems too thick, add reserved pasta water a tablespoon at a time. Let it simmer for another 2 minutes so the flavors meld together.