If you’re vegetarian try Főzeléks which is vegetables simmered usually in water and thickened with roux. Try tökfőzelék (marrow with dill and sour cream), or finomfőzelék (mixed vegetables thickened with white sauce).
In restaurants they are served with stew, pork chop, or fried eggs depending of the type of the Főzelék. Smoked meat or sausage is essential for the cooking of some Főzeléks, like Babfőzelék (made from beans). If you’re a strict vegetarian ask the waiter before ordering a főzelék that whether meat or meat stock was used during its preparation.