Prep the chicken. Pat the chicken dry.
If using thick breasts, slice horizontally into cutlets for even cooking. Season both sides with salt, pepper, and Italian seasoning. Lightly dredge in flour, shaking off any excess.
Heat the pan. Set a large skillet over medium-high heat.
Add the olive oil and 1 tablespoon butter. When the butter foams, it’s ready for the chicken.
Sear the chicken. Lay the chicken in the pan without crowding. Sear 3–4 minutes per side, until golden and just cooked through (165°F/74°C).
Transfer to a plate and tent with foil.
Build the flavor base. Lower heat to medium. Add the remaining tablespoon of butter. Stir in the minced garlic and cook 30–60 seconds until fragrant.
Don’t brown the garlic.
Deglaze. Pour in the chicken broth. Scrape up any browned bits with a wooden spoon. Let it simmer 2 minutes to reduce slightly.
Make it creamy. Stir in the cream.
Bring to a gentle simmer, not a hard boil. Cook 2–3 minutes to thicken slightly.
Add Parmesan and lemon. Reduce heat to low. Whisk in the Parmesan until melted and smooth.
Add lemon zest and 1 teaspoon lemon juice. Taste and adjust salt and pepper. If you want a thicker sauce, whisk in the cornstarch slurry and simmer 1 minute.
Finish the chicken. Return the chicken and any juices to the skillet.
Spoon sauce over the top and simmer 2 minutes, just to warm through and let flavors meld.
Garnish and serve. Sprinkle with fresh herbs and a pinch of red pepper flakes if using. Serve with pasta, mashed potatoes, rice, or crusty bread. Add extra Parmesan at the table.