Sounds a little more like kleftiko (but I’m not sure, there are other slow-braised/baked clay pot dishes ) 
Giouvetsi in Greece, while named after the cooking vessel, is usually braised meat or poultry, with tomato and orzo. Looks like this.
The cheese spread, should you want to order it again, is called tyrokefteri / tirokefteri, Htpti or Kopanisti. It’s feta blended with hot peppers. Some people are really proud do their recipe.
Another nice feta starter is feta sto fournou, which is baked feta and tomatoes.
