In a food processor, pulse mushrooms until ï¬nely chopped. Heat a large skillet to medium-high. Add 1 tsp oil; add beef and mushrooms and spread out to cover the pan. Sear 6 to 7 minutes, or until mixture starts to brown. Break up meat and continue to cook until no longer pink, about 10 minutes. Remove beef and mushrooms, leaving as much fat in the pan as possible. Add onions to skillet and cook until translucent, about 10 minutes. Add tomato paste and cook until dark red, about 3 minutes. Stir in garlic; cook 30 seconds. Stir beef and mushrooms into tomato and onion mixture. Add apple juice, scraping any browned bits up from bottom of pan. Put ketchup, tomatoes, soy sauce and sugar in skillet; stir and bring to a simmer. Cook until thickened, about 15 minutes. Season with salt and pepper. Scoop beef mixture onto buns; top with banana peppers. Serve with a spoon.