1. Preheat your oven to 375°F (190°C).
2. Prepare the chicken by pounding each breast to an even thickness, about 1/2 inch. This ensures even cooking.
3. In a shallow dish, combine the flour, salt, and pepper. In another dish, have the beaten eggs ready. In a third dish, place the grated parmesan cheese.
4. Dredge each chicken breast first in the flour mixture, then dip it into the beaten eggs, and finally coat it with parmesan cheese, pressing gently to adhere.
5. Heat olive oil in a large oven-safe skillet over medium-high heat. Add the chicken breasts and cook until golden brown on each side, about 3-4 minutes per side.
6. Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and the internal temperature reaches 165°F (75°C).
7. While the chicken bakes, melt the butter in a saucepan over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.
8. Pour in the heavy cream and chicken broth, stirring well. Let the sauce simmer until slightly thickened, about 5 minutes.
9. Remove the chicken from the oven and pour the garlic cream sauce over the top. Garnish with fresh parsley if desired.

My abuela always taught me the importance of patience in cooking. Letting the sauce simmer allows the flavors to meld beautifully, creating a delightful harmony that elevates the entire dish.