Cut each chicken breast in half lengthwise to get thinner cutlets. Over plastic wrap, slightly pound the chicken to even thickness as needed using a meat mallet. This is for even cooking and to tenderize the chicken a bit.
Season both sides of the chicken cutlets with salt, pepper, and Italian seasoning (per chicken cutlet, use about ¼ teaspoon each: Kosher salt, ground black pepper, Italian herb seasoning). Dredge the seasoned chicken in flour and shake off any excess.
Heat some olive oil in a large nonstick skillet over medium heat. Cook prepared chicken on both sides, about 4-5 minutes per side, until golden brown or until internal temperature reaches 165 degrees F. Remove chicken from pan and set aside.
Don’t wipe the pan clean. Melt 2 tablespoons unsalted butter, then add garlic, and cook until fragrant. Add chicken broth and 1 tablespoon lemon juice. Taste it, and add the second tablespoon of lemon juice if desired (I ended up adding 2 tablespoons). Bring to a light simmer. Then, stir in heavy cream plus salt and pepper to taste until evenly combined.
Return chicken to pan and bring to a simmer. Simmer for another 4-5 minutes until the sauce has thickened a bit.
Serve with lemon slices and freshly chopped parsley. Enjoy!