Season the chicken with salt and pepper, then coat each piece in flour, shaking off any excess. Heat the olive oil in a large skillet over medium heat and melt 1 tablespoon of butter, swirling the pan to evenly combine the oil and butter. Add the chicken cutlets to the skillet. Cook the chicken without overcrowding the pan, working in batches if necessary, browning each side for 4-5 minutes until golden and fully cooked. Remove the chicken from the skillet, place it on a plate, cover, and set aside. In the same skillet, melt the remaining 1 tablespoon of butter and sauté the minced garlic for about a minute until fragrant. Pour in the chicken stock, scraping the bottom of the pan with a wooden spoon to loosen any browned bits. Reduce the heat to medium-low and stir in the heavy cream, lemon juice, and grated Parmesan cheese. Let the sauce simmer gently for a few minutes. Season with salt and pepper to taste, then return the chicken to the skillet, allowing it to simmer in the sauce until the sauce thickens slightly. Garnish with chopped fresh parsley and serve warm over pasta, mashed potatoes, or rice.