In a large lidded skillet, heat the oil and saute the carrot, celery, onion, garlic and potato for 5 minutes. Add salt, pepper and white wine. Allow to bubble for a few minutes. Reduce the heat to a simmer and cover. Simmer for 15 minutes. Add 1/2 cup water if necessary.
Arrange the cooked patties over the simmered vegetables in a single layer. Arrange the tomato and lemon slices evenly over the top of the patties. Sprinkle with parsley and additional salt and pepper. Cover and simmer for 5 minutes or until patties are hot. Add a bit of water if necessary, but the finished dish should be rather dry.
Remove from the heat, uncover and allow to cool. Carefully transfer to a serving plate and garnish with fresh lemon slices or wedges and parsley if desired. Chill.
Serves 4 to 6 as a main dish.