For the jam:
4 thick slices applewood-smoked bacon, cut crosswise into ½-inch strips
1 large red onion, halved and thinly sliced
Kosher salt and freshly ground black pepper
⅓ cup balsamic vinegar
½ teaspoon Dijon mustard
⅓ cup water
For the burgers:
2 thick slices applewood-smoked bacon
1½ pounds ground beef (85% lean)
½ teaspoon Worcestershire sauce
1 teaspoon Kosher salt
½ teaspoon freshly ground black pepper
4 hamburger buns, split
Sliced Gruyere cheese, optional
Start by making the jam. Cook the bacon in a large skillet set over medium heat until lightly browned but not crisp, about 8 minutes. Use a slotted spoon to transfer to paper towels to drain. Discard all but about 2 tablespoons of oil from the skillet.
Add the onion to the skillet, season with salt and pepper to taste, cover and cook for 2 minutes. Uncover and add a splash of water, then scrape up any browned bits from the bottom of the skillet. Cover and continue cooking, stirring occasionally, until the onions are soft, about 10 minutes. Stir in the vinegar, mustard and water.
Return the bacon to the skillet and simmer until the liquid has thickened and most of it has been absorbed, 2-4 minutes. Transfer the jam to a small bowl, let cool slightly and cover with plastic wrap. The jam can be left at room temperature or refrigerated for up to 2 days. If refrigerated, gently reheat before serving.
To make the burgers, mince the bacon. Transfer to a large bowl, then add the beef, Worcestershire, salt and pepper. Gently combine until well mixed but not overworked. Form into 4 equal patties, each about ¾-1-inch thick. Using your thumb, make a deep depression in the center of each patty to prevent them from swelling during cooking.
Heat a gas or charcoal grill to medium-high heat (400-450º). Grill the burgers over direct heat until grill marks form, 4-5 minutes. Flip and continue cooking an additional 4 minutes for medium doneness. For more well done burgers, cook an additional minute. As the burgers are finishing up, add cheese if desired. Transfer to a plate and tent with aluminum foil. Toast the buns on the grill for about 1 minute. Top each burger with about ¼ cup of jam and serve immediately.