Heat a skillet over medium-low heat and melt 1 tablespoon of butter until it begins to bubble slightly. Add the sliced onion, spreading it out into an even layer. Stir to coat with the butter.

Sprinkle in ½ teaspoon of brown sugar to encourage caramelization and enhance sweetness. Cook slowly, stirring every few minutes. Let the onions sit between stirs so they develop that deep golden color. Keep the heat on medium-low to prevent burning.

Continue for about 25–30 minutes, or until the onions are soft, sweet, and a rich amber color. If they start to dry out or brown too quickly, add a splash of water and lower the heat slightly. Set aside.

While the onions caramelize, spread the remaining butter over the cut sides of the buns. Place on a baking sheet and broil until buns are toasted and golden brown. Set aside.

Cut shallow slits diagonally accross opposite sides of the hot dog. This prevents it from curling up or bursting. They also allow heat to penetrate deeper, which can shorten cooking time and give it a nice caramelized edge where the cuts open up. Cook on a grill for 5-7 minutes.