Heat the oven to 350ºF.
In a large saucepan, sauté the onion, carrots, and garlic for 3-4 minutes or until they start to soften.Add mushrooms and garlic and cook for 5 minutes. Let cool slightly.
Add the cooked vegetables, rice, walnuts, parsley, and seasonings to a food processor. Process until a crumbly mixture forms, 20-30 seconds, scraping down the sides as needed. Adjust the seasoning to taste.
Form the mixture into 4 large balls. Roll the balls in flour until they're lightly coated, then flatten them into patties (about ½ inch to ¼ inch thick).
Melt the butter in your sauté pan. One by one, place the cut sides of the rolls into the melted butter to coat them. Place on a baking sheet, buttered side up. Season with garlic powder. Bake 5 minutes, or until lightly toasted. Place the mozzarella on the top half of the rolls; cook 3-4 minutes or until the cheese starts to melt.
In the same pan, cook the veggie burgers for 5 minutes on each side.
To serve, place a veggie burger on a "bottom" roll. Cover with 2 tablespoons warmed marinara. Top with a "top" roll, cheese side down.