Add the butter to a large, heavy-bottomed pot with a lid over medium heat (I use a 5-qt Dutch oven). Once melted, add the sliced Vidalia onions, stirring to coat. Cover the pot. Cook 12-15 minutes, until softened & fragrant. The onions shouldn’t require too much attention at this point, but feel free to uncover & stir occasionally.
Once softened, uncover the pot & reduce heat to medium-low. Season the onions with 2 teaspoons kosher salt, stirring to combine. Continue to cook, stirring occasionally, until tender, fragrant, & deeply browned, 30-45 minutes more. Helpful hints: Be sure to adjust heat as needed to allow the onions to caramelize slowly & prevent burning. The closer the onions get to reaching caramelization, the more often you will want to stir to promote even browning & prevent burning.
Once the onions are caramelized, deglaze the skillet. Slowly pour in the dry sherry, using a wooden spoon to scrape up any browned bits formed on the bottom of the pan. Increase the heat to medium-high to bring the wine to a simmer, then simmer 2-3 minutes or until reduced. Remove from the heat & set aside to cool slightly for caramelized onion burger assembly or store in an airtight container in the refrigerator for up to 1 week.
To a large mixing bowl, add the ground beef, caramelized Vidalia onions, Worcestershire sauce, Dijon mustard, & garlic powder. Season with S&P as desired. Use your hands to mix until just combined – taking care not to overmix. Divide the burger mixture into 4 portions. Form each portion into a burger patty slightly larger than the size of your buns, pressing a small indent in the center of each patty. Place patties on a plate or a small baking sheet & set aside.
Preheat the grill to medium heat, about 450-500 degrees F. Use grilling tongs to run oiled paper towels over the grill grates, generously oiling them. Place the burgers directly on the grill grates. Grill 3-5 minutes per side, keeping the grill lid closed as the burgers cook. If you’d like to top your caramelized onion burgers with cheese, do so when there are 2 minutes left of grilling time. Once cooked to desired doneness, transfer the burgers to a small baking sheet or plate & let rest for a couple minutes before serving.