Heat oil in small non-stick skillet over low heat. Add sliced onions and stir occasionally until golden (will take about 15 -20 minutes). Take off heat and proceed with sandwiches or let cool and store in the refrigerator for up to a week.
Cut each half dog in half and then slit each half into two, vertically <--- you will get 4 pieces per hot dog and a total of 16 pieces (refer pictures). This size makes them perfect for sandwich bread.
Stir together barbecue sauce and dijon mustard in a small bowl, until smooth.
Working with one sandwich at a time, take 2 slices of bread, spread some mayonnaise on one side of each slice and place mayo side down on a plate.
Spread one-third of barbecue sauce-mustard mixture on one slice (non-mayo side). Followed by one-third caramelized onions, then ½ cup of cheddar and then arrange 5 pieces of cut hot dogs in a single layer. Top with other bread slice (mayo side up).
Place a cast-iron or non-stick pan over medium heat. Once hot, carefully transfer sandwiches (holding them on both sides). Cook until deep golden on both sides (occasionally press sandwich with a wide spatula while cooking to help them adhere well and crisp up).
Remove sandwich on to a plate and proceed with remaining two sandwiches.
Notes
Recipe adapted from a similar combination of flavors that I found online several years ago. Unfortunately, I couldn't find it anymore, hence I came up with my creation