Pat the chicken dry with paper towels and season both sides generously with salt, pepper, and Italian seasoning.

Heat oil and butter in a large skillet over medium-high heat until butter foams.

Place the seasoned chicken breasts in the hot pan and sear, undisturbed, for 4-5 minutes per side until golden.

Transfer to a plate and tent with foil.

Reduce heat to medium and add garlic to the skillet. Sauté for 30-45 seconds until fragrant.

Deglaze with 1/2 cup chicken stock, scraping up browned bits.

Add remaining chicken stock and heavy cream, stirring to combine and bring to a gentle simmer.

Whisk in grated Parmesan until melted and smooth, then season with Dijon mustard, lemon juice, salt, and pepper to taste. Simmer for 3-5 minutes until the sauce thickens slightly.

Nestle the seared chicken back into the skillet, spooning sauce over each breast.

Cover and simmer on low for 6-8 minutes until chicken reaches an internal temperature of 155-160°F.

Remove chicken, turn off the heat, and finish the sauce with chopped parsley.

Taste and adjust seasoning as needed.

If a thinner sauce is desired, stir in a splash more chicken stock; for thicker, reduce uncovered for 1-2 minutes.

Let chicken rest for 5 minutes before slicing against the grain.

Serve hot with extra Parmesan and a sprinkle of parsley.