Pat the chicken breasts dry with paper towels, then halve them horizontally to create even cutlets about 3/4-inch thick. In a small bowl, combine garlic powder, Italian seasoning, salt, and pepper. Season both sides of each cutlet generously with this mixture, pressing gently so it adheres. Let the seasoned chicken sit at room temperature for 5-10 minutes while you prepare the remaining ingredients.
Heat olive oil in a large skillet over medium-high heat until shimmering, about 2 minutes. Working in batches if needed to avoid crowding, place the seasoned chicken cutlets in the hot oil and sear for 5-6 minutes until golden brown on the first side. Flip and cook for another 4-5 minutes until the second side is golden and the internal temperature reaches 165°F. Transfer the cooked chicken to a clean plate and set aside.
In the same skillet (don't rinse it—those browned bits add flavor), melt butter over medium heat. Add the freshly minced garlic and cook for 30 seconds until fragrant, then sprinkle flour over the garlic and stir constantly for 1 minute to create a light roux. Pour in the chicken broth and bring to a simmer, stirring occasionally and scraping up any browned bits from the pan bottom. Simmer for 5 minutes until the mixture thickens slightly.
Remove the skillet from heat and pour in the heavy cream, stirring to combine fully. Return the pan to low heat and simmer gently for 2-3 minutes, stirring occasionally, until the sauce reaches a silky consistency. Remove from heat again and add the freshly grated parmesan cheese, stirring until completely melted and smooth—I like to use freshly grated parmesan because pre-shredded cheese contains anti-caking agents that prevent it from melting as smoothly. Taste the sauce and season with lemon juice, red pepper flakes, and additional salt and pepper as needed.
Return the seared chicken and any accumulated juices from the plate to the skillet with the creamy sauce. Cook over low heat for 2 minutes, gently turning the chicken to coat it evenly with the sauce and ensure it's heated through. Transfer the chicken to serving plates and spoon the sauce generously over each piece. Garnish with fresh parsley and serve immediately over your choice of potatoes and greens.