Pat the chicken breasts completely dry with paper towels, then season both sides generously with salt and black pepper.

Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until the butter stops foaming. Add the chicken breasts and sear for 5 to 6 minutes per side until deeply golden and the internal temperature reaches 165°F. Remove to a plate and let rest for at least 5 minutes.

Reduce the heat to medium and melt the remaining 2 tablespoons of butter in the same skillet. Add the minced garlic and cook for about 30 seconds, stirring constantly, until fragrant but not browned.

Pour in the chicken broth and scrape up all the browned bits from the bottom of the pan. Stir in the heavy cream and let the mixture simmer gently for 3 to 4 minutes until slightly thickened.

Gradually whisk in the Parmesan cheese, adding about half a cup at a time and stirring until completely melted before adding more. Simmer for 2 more minutes, then season with salt and pepper to taste.

While building the sauce, bring a large pot of salted water to a boil and cook the twisted pasta until al dente, typically 8 to 10 minutes. Reserve 1 cup of the starchy pasta water before draining.

Slice the rested chicken into strips and return it to the skillet along with any accumulated juices. Add the drained pasta and toss everything together until the noodles are completely coated. If the sauce seems too thick, add the reserved pasta water a few tablespoons at a time.

Garnish with fresh chopped parsley and serve immediately while the sauce is creamy and hot.