Wash the meat, dab dry and cut into strips. Peel onions and cut into slices. Thyme wash, pluck. Mix everything well with 3 tablespoons of oil and gyros spice. Cover and let it stand for at least 1 hour.
Peel, wash and grate the carrots. Clean, wash and slice spring onions into rings. Fold both into the coleslaw.
Heat a pan without fat. Fry the gyros in it for 3-4 minutes in portions. Add just under 1⁄4 l water, cream and processed cheese, bring to the boil. Season with salt and pepper.
Pour the gyros and sauce into a greased casserole dish. Bake in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer) for approx. 30 minutes. Crumble the feta. Mix with crème fraîche and spread on the gyros. Bake at the same temperature for another 10 minutes. Serve with coleslaw. Flatbread tastes good with it.