In a large saucepan over low heat stir together the barbeque sauce, beans, chili seasoning, brown sugar, and mustard. Bring to a boil and reduce heat to a simmer and cook for 10 to 12 minutes, stirring occasionally.
Meanwhile, set up grill or indoor grill pan for direct cooking over medium heat. When ready to start cooking oil the grate. Place hot dogs on the hot, oiled grill. Cook for 10 minutes or until heated through, turning occasionally. Toast buns on grill, if desired. Place hot dogs in buns and top with chili. Serve hot with chopped white onions. (Reserve leftover chili for Round 2 Quesadilla recipe)