For the balsamic onions: Combine the bacon and duck legs in a large saute pan over medium heat. Saute until the bacon and duck skin have rendered their fat and become crispy, 5 to 7 minutes. Remove from the pan and set aside to cool, leaving the rendered fat in the pan; you want about 3 tablespoons of fat. When cool enough to handle, separate and chop up the skin from the duck legs. Combine the duck skin with the bacon and set aside. Shred the duck meat into bite-size pieces and reserve separately.
Add the sweet onions to the pan with the rendered fat and cook over medium heat, stirring occasionally, until golden brown and caramelized, 20 to 30 minutes. Add the garlic and cook another 2 minutes. Add the balsamic vinegar and sugar, raise the heat and cook until the onions become jam-like, another 5 to 7 minutes. Add the bacon and duck skin to the onions, mix and set aside.
Preheat the oven to 400 degrees F.
Lay the puff pastry out on a floured surface. Using a 1 3/4-inch cutter, punch out 16 rounds of puff pastry. Lay the rounds on a baking sheet, then place another clean baking sheet on top of the rounds to keep them flat while baking. Transfer to the oven and bake until golden brown, about 10 minutes. Set aside.
Lower the oven temperature to 350 degrees F.
Smear each puff pastry round with whole-grain mustard. Add a pile of balsamic onions, some shredded duck meat and a sprinkling of Gruyere, and top it off with a piece of hot dog. Return to the oven to warm everything through and melt the cheese, about 5 minutes. Finish with some pickled red onions and serve. Oh my!