Start by laying out the butterflied chicken breasts on a clean surface. Ensure they are evenly spread out for easy seasoning. Season both sides of each chicken breast with white pepper, adding a delightful kick to the dish. Place a slice of prosciutto and a spoonful of Fontina cheese on each chicken breast. This combination will contribute rich and savory flavors to the dish. Roll up the chicken breasts, securing them with toothpicks to maintain their shape during cooking. This step is crucial for the presentation and ensures the stuffing stays intact.

In a large skillet, melt 4 tablespoons of unsalted butter over medium heat. This will serve as the flavorful base for cooking the chicken. Add the rolled-up chicken breasts to the skillet and cook for 4-5 minutes on each side or until they achieve a golden brown exterior. This searing process locks in the juices, enhancing the overall taste. Remove the cooked chicken breasts from the skillet and set them aside, allowing for the next steps in the cooking process.

In the same skillet, melt the remaining 4 tablespoons of unsalted butter, creating a luscious base for the sauce. Add garlic cloves and diced onion to the skillet, sautéing until they become fragrant. This step adds aromatic layers to the dish. Introduce sliced cremini mushrooms to the skillet, cooking them until tender and golden brown. This brings a savory and earthy dimension to the sauce. Pour in dry white wine, letting it simmer for a couple of minutes. The wine contributes depth and complexity to the sauce. Squeeze the juice of 2 lemons into the skillet, stirring to combine. The citrusy brightness will balance the richness of the dish.

Return the cooked chicken breasts to the skillet, ensuring they are well-coated with the flavorful garlic and mushroom sauce. Sprinkle chopped fresh basil over the chicken breasts, adding a burst of freshness to the dish. Reduce the heat to low and let the dish simmer for an additional 5-7 minutes, allowing the flavors to meld together and create a cohesive taste profile. Before serving, remember to remove the toothpicks from the chicken breasts to ensure a safe and enjoyable dining experience.