In a medium skillet or saucepan, combine brown sugar, soy sauce, mirin, and sake. Bring to a simmer and cook for 2-3 minutes to burn off the alcohol.
In a separate bowl, mix cornstarch and water into a slurry.
Add slurry to the skillet and stir well. Continue cooking 2-3 more minutes or until the teriyaki sauce has reached your desired thickness to glaze your hot dogs. Set sauce aside and let cool while you prepare your hot dogs.
Grill your hot dogs, brushing on some teriyaki sauce in the last minute of cooking. Toast hot dog buns, if desired.
Assemble your Japadogs by placing your hot dog in a bun and topping with more teriyaki sauce. Add Japanese mayonnaise on top (I like to do a zig zag pattern), shredded seaweed, bonito flakes, and green onion to taste. Serve and enjoy!