Cook the pasta according to package directions until al dente. Reserve about 1 cup of the pasta water before draining. Set the drained pasta aside.
Season the chicken pieces lightly with salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
Reduce the heat to medium. Add the minced garlic to the same skillet and cook for 30 seconds until fragrant. Do not let the garlic burn.
In a small bowl, whisk together the honey, soy sauce, and apple cider vinegar to create the honey garlic glaze. Pour this mixture into the skillet. Let it bubble for 1 minute, scraping up any browned bits from the bottom of the pan.
Stir in the chicken broth and Italian seasoning. Bring the mixture to a simmer.
Lower the heat to medium-low. Slowly whisk in the heavy cream until the sauce is smooth. Continue to cook, stirring often, until the sauce begins to thicken slightly, about 3 minutes.
Stir in the grated Parmesan cheese until fully melted and incorporated into the sauce. If the sauce is too thick, add a splash of the reserved pasta water until you reach your desired consistency.
Return the cooked chicken to the skillet. Toss to coat the chicken in the sauce.
Add the cooked pasta to the skillet and toss everything together until the pasta is evenly coated with the sauce. Add more pasta water if needed to loosen the sauce.
Serve immediately, garnished with fresh parsley.
Notes
For a thicker sauce, simmer the cream mixture for a few extra minutes before adding the cheese.
If you prefer a milder garlic flavor, use 3 cloves of garlic instead of 4.
You can substitute chicken thighs for chicken breasts if you prefer darker meat.