Saute onion and green peppers then add in garlic. Add beef and spices. Stir in tomatoes, Worcestershire sauce, vinegar, brown sugar, sriracha and mustard. Bring to a simmer then reduce heat to low for 20 minutes.
Brush Texas toast with garlic butter then place buttered side down in the skillet. Add one slice of cheese to one slice then the sloppy joe mix on the other slice. Cook until cheese is melty and bread is golden brown.