Heat 2 tablespoons of the butter in large skillet over medium heat until melted. Add the red pepper and shallots and gently cook until the shallots soften, about 3 minutes. Add the mushrooms and season with salt and pepper. Cover and cook for 10 minutes, then take off the cover and cook until the mushrooms are golden brown, another 10 minutes. Add the thyme and garlic and cook until fragrant, then deglaze with the wine and cook until the alcohol scent dissipates, another 2 to 3 minutes. Add the remaining 2 tablespoons butter and cook until melted; season again. Serve over steak, pork chops or chicken.