Start by pounding the chicken breasts until they are even in thickness. Season both sides with salt and pepper, then lightly coat them in flour. This helps create a golden crust when cooked.
Heat olive oil in a large skillet over medium heat. Add the chicken and cook until golden brown on both sides and fully cooked through. Remove from the skillet and set aside.
In the same skillet, melt butter and add minced garlic. Cook for about a minute until fragrant, making sure not to burn it. This step builds the foundation of flavor for the sauce.
Pour in chicken broth and stir well, scraping any browned bits from the pan. Add heavy cream, lemon juice, lemon zest, and Italian seasoning. Let it simmer gently to thicken.
Stir in freshly grated parmesan cheese until it melts completely into the sauce. The sauce should become smooth, creamy, and slightly thickened.
Return the cooked chicken to the skillet and coat it well with the sauce. Let it simmer for a few minutes so the flavors blend together perfectly.