Cut the bell peppers and mushrooms into small pieces. Heat oil in a pan over medium-high heat and fry the peppers and mushrooms for 3 minutes. Remove from the pan and set aside. Add the gyros meat to the same pan and fry for 3-4 minutes until heated through. Return the peppers and mushrooms to the pan. Add the white wine, tomato paste, and sour cream. Stir to combine.
Transfer everything to a baking dish and sprinkle the 100 g grated cheese over the top. Bake in a preheated oven at 175°C (347°F) with conventional heat for 15 minutes.