Bring a large pot of salted water to boil and add pasta, cooking according to package directions. Reserve 1 cup of pasta water before draining—starches in this reserved liquid help create silky sauce consistency when mixed back in later.
While pasta cooks, pat chicken pieces dry with paper towels and season with salt, pepper, and Italian seasoning. Heat olive oil in a large skillet over medium-high heat, then sear chicken for 3-4 minutes per side until golden brown and cooked through. Remove to a plate.
Add 3 tbsp butter to the same skillet and reduce heat to medium, then add minced garlic and cook for 1-2 minutes until fragrant. Stir constantly to prevent burning—the garlic should be pale golden, not brown.
Pour in chicken broth and scrape up any brown bits from the pan bottom using a wooden spoon. Return cooked garlicky buttery chicken pasta components to the skillet by adding chicken pieces back to the pan, then simmer for 2-3 minutes until flavors meld together beautifully.
Reduce heat to low and stir in heavy cream, remaining 3 tbsp butter, lemon juice, and red pepper flakes. Cook for 1-2 minutes until cream is warmed through but not boiling.
Add drained pasta to the skillet and toss constantly, adding reserved pasta water a few tablespoons at a time until sauce reaches desired consistency. Fold in grated parmesan and fresh parsley, then taste and adjust seasoning with additional salt and pepper as needed.