Heat oil in a large skillet over medium heat. Add the onion and bell pepper and cook for 3-5 minutes, until translucent.
Add the minced garlic and cook for an additional minute, stirring to ensure the garlic does not burn. Then, add the ground beef and break up any clumps. Cook for 8-10 minutes, until ground beef is cooked through.
While the ground beef is cooking, mix together tomato sauce, tamari sauce, apple cider vinegar, brown sugar, ground mustard, salt and black pepper. Stir to combine.
Taste and add an additional tablespoon of brown sugar if you would like it sweeter.
Once the ground beef is browned and cooked through, stir in the tomato sauce mixture. Cook for 5 or so minutes, stirring occasionally, until the sauce is warm.
Serve as lettuce wraps, topped with chopped green onions.