Heat a large skillet over medium-high heat.
Place 1 tortilla onto a clean work surface. Sprinkle with 2 tablespoons of the cheese. Top with 1/2 cup of the bean chili and sprinkle with 2 more tablespoons of the cheese. Put another flour tortilla on top and carefully place in the skillet. Cook for 3 minutes until tortilla is slightly browned and cheese starts to melt. Flip and cook for another 3 minutes on the other side. Repeat with remaining ingredients. Transfer quesadillas to a cutting board. Cut into wedges and serve with sour cream or salsa.
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.