Whisk together vegenaise, onion, parsley, tarragon, and mustard in a bowl.
Mash tofu in with a fork. Stir in mushrooms, carrots, and sun-dried tomatoes. Fold in breadcrumbs.
Heat large skillet coated with oil over medium heat. Scoop tofu mixture into patties (1/4 cup at a time) Cook until golden. Flip and cook 4 to 5 minutes more.