In a medium bowl, combine goat cheese, cream cheese, sun-dried tomatoes, basil, thyme, garlic, lemon zest, 1/4 tsp salt, and 1/8 tsp pepper. Mix thoroughly until fully incorporated. Refrigerate for 15 minutes to firm slightly while preparing chicken.
Place chicken breast on cutting board. With palm flat on top, use sharp knife to cut horizontally through the breast, stopping 1/2 inch before cutting all the way through. Open like a book. Cover with plastic wrap and pound to even 1/4-inch thickness using textured side of meat mallet.
Season inside surface with remaining salt and pepper. Place 2-3 tablespoons of filling mixture in center of each breast, leaving a 1-inch border around edges.
Starting from narrow end, roll chicken tightly around filling. Lay 2-3 slices of prosciutto slightly overlapping on work surface. Place rolled chicken seam-side down on prosciutto. Wrap prosciutto around chicken, overlapping slightly. Secure with butcher's twine at 1-inch intervals (or toothpicks if preferred).
Allow wrapped chicken to rest at room temperature for 15 minutes. Preheat oven to 375°F (190°C).
Heat olive oil in oven-safe skillet over medium-high heat until shimmering. Sear chicken on all sides until prosciutto is crisp and golden, about 2 minutes per side.
Transfer skillet to preheated oven. Roast until internal temperature reaches exactly 165°F (74°C) at thickest point, approximately 12-15 minutes.
Remove from oven and transfer to cutting board. Tent loosely with foil and rest for 5 minutes. Remove twine or toothpicks, slice into medallions, and serve.