Prepare a charcoal fire or preheat the broiler. In an 8- to 10-inch skillet, heat 2 tablespoons of the olive oil over medium heat. Add the garlic and sauté slowly until browned on all sides, shaking the pan to keep them moving, about 10 minutes. Add the sweet and dry wines and cook at a low boil until the liquid is reduced to 1/4 cup, about 15 minutes. The garlic should be very soft at this point. Set aside.
Season the lamb chops with salt and pepper and grill or broil until medium rare, 4 to 5 minutes per side.
Heat the remaining 3 tablespoons of olive oil in 12- to 14-inch sauté pan over high heat. Add the mushrooms and sauté over high heat until brown and soft, 3 to 4 minutes. Add the garlic and wine reduction to the mushrooms and stir to coat. Stir in the mint leaves and remove from the heat. Season the mushroom and garlic mixture with salt and pepper and spoon onto the center of each plate. Top with lamb chops. Serve immediately.
Wine pairing: Merlot or Cab Fran-Merlot Blend