Heat a large pan over medium-high heat. Sear the ready-made gyros meat (1,300g) for 5 minutes until browned on the sides. Transfer to a baking dish.
To the same pan with the drippings, add cream (200ml) and cream cheese (100g) over medium heat. Bring to a boil, stirring constantly, until the cheese has melted completely (about 3-4 minutes).
Season the sauce with salt, pepper, and cayenne pepper to taste. Add Metaxa to taste. Continue heating.
Stir in sauce thickener according to package directions until the sauce reaches a thick consistency. Cook for 2 minutes.
(Optional) Pour a splash of Metaxa over the meat in the baking dish if desired.
Pour the sauce over the meat. Cover generously with Gouda and/or Mozzarella cheese.
Bake in a preheated oven at 170°C (340°F) for 12-15 minutes until the cheese has melted and turned golden.