Bring a large pot of salted water to a boil. Cook the linguine according to package directions until al dente. Reserve 1/2 cup of the pasta water, then drain and set the pasta aside.

Heat the olive oil in a large skillet over medium heat. Season the chicken pieces with salt and pepper. Add the chicken and cook, stirring occasionally, until browned and cooked through, about 5–7 minutes. Remove the chicken to a plate.

In the same skillet, add the butter. When melted, add the minced garlic and sauté for about 1 minute until fragrant—don’t let it brown.

Pour in the heavy cream and bring it to a gentle simmer. Stir in the Italian seasoning.

Lower the heat and gradually add the shredded cheddar and grated Parmesan, stirring constantly until the cheeses melt into a smooth sauce. If the sauce seems too thick, add a splash of the reserved pasta water to loosen it.

Return the cooked chicken to the skillet. Add the drained linguine and toss everything together over low heat. Add reserved pasta water a little at a time until the sauce reaches your desired consistency and coats the pasta.

Taste and adjust with salt and pepper. Serve immediately, topped with chopped fresh parsley.