Servings: 4 to 6

2 pounds yellow onions (about 2 large or 4 medium) 2 pounds yellow onions (about 2 large or 4 medium)
1 small bunch fresh thyme 1 small bunch fresh thyme
2 cloves garlic 2 cloves garlic
6 ounces Gruyère cheese, divided 6 ounces Gruyère cheese, divided
1/2 cup panko breadcrumbs ½ cup panko breadcrumbs
1/2 cup whole or 2% milk ½ cup whole or 2% milk
1 large egg 1 large egg
2 teaspoons Worcestershire sauce 2 teaspoons Worcestershire sauce
2 1/2 teaspoons kosher salt, divided, plus more as needed 2 ½ teaspoons kosher salt, divided, plus more as needed
3/4 teaspoon freshly ground black pepper, divided, plus more as needed ¾ teaspoon freshly ground black pepper, divided, plus more as needed
1 1/2 pounds ground beef 1 ½ pounds ground beef
2 tablespoons unsalted butter 2 tablespoons unsalted butter
2 tablespoons all-purpose flour 2 tablespoons all-purpose flour
1/2 cup dry white wine ½ cup dry white wine
1 (14.5-ounce) can beef broth (scant 2 cups) 1 (14.5-ounce) can beef broth (scant 2 cups)
1 teaspoon balsamic or sherry vinegar 1 teaspoon balsamic or sherry vinegar
Crusty bread, for serving (optional) Crusty bread, for serving (optional)

Arrange one oven rack 6 to 8 inches from the broiler and a second rack in the middle of the oven. Heat the oven to 400°F. Line a rimmed baking sheet with parchment paper or a silicone baking mat.
Halve and thinly slice 2 pounds yellow onions (about 7 cups). Pick the leaves from 1 small bunch fresh thyme until you have 2 tablespoons. Mince 2 garlic cloves. Grate 6 ounces Gruyère cheese on the large holes of a box grater (about 1 ½ cups).
Place the garlic, 2 teaspoons of the thyme, ¼ cup of the Gruyère cheese, ½ cup unseasoned dried breadcrumbs or panko, ½ cup whole or 2% milk, 1 large egg, 2 teaspoons Worcestershire sauce, 1 ¼ teaspoons of the kosher salt, and ¼ teaspoon black pepper in a large bowl and stir to combine. Add 1 ½ pounds ground beef and use your fingers to combine the meat and flavorings. Handle the meat gently and do not overmix.
Form the mixture into 32 to 34 (about 1 ½-inch) meatballs (about 2 tablespoons each). Place on the baking sheet, spacing them about ¾-inch apart.
Bake on the middle rack until browned and cooked through or until an instant-read thermometer inserted into the center of a meatball registers at least 165°F, 15 to 20 minutes. Meanwhile, make the sauce.
Melt 2 tablespoons unsalted butter in a 12-inch cast iron or other broiler-safe, heavy-bottomed skillet over medium heat. Add the onions, 1 tablespoon of the thyme, remaining 1 ¼ teaspoons kosher salt, and remaining ½ teaspoon black pepper. Cook, stirring frequently with a wooden spoon and reducing the heat if the onions start to burn, until the onions have reduced by over half, are very soft, and deep golden-brown, 25 to 30 minutes.
Sprinkle 2 tablespoons all-purpose flour over the onions and stir until the flour is completely incorporated and leaves a film on the bottom of the skillet and begins to brown, about 1 minute. Add ¼ cup dry white wine and scrape up any browned bits on the bottom of the skillet. Continue to stir until the wine is evaporated, about 30 seconds.
Add 1 (14.5-ounce) can beef broth and whisk to combine. Increase the heat back to medium if it was lowered while cooking the onions. Bring to a boil and cook until the sauce thickens enough to coat the back of a spoon, 6 to 8 minutes. Remove the pan from the heat. Add 1 teaspoon balsamic or sherry vinegar and stir to combine. Taste and season with more kosher salt and black pepper as needed.
Remove the meatballs from the oven. Set the oven to broil. Using tongs or a slotted spoon, transfer the meatballs to the sauce. Gently stir to coat the meatballs in the sauce, then spread into an even layer. Sprinkle with the remaining 1 ¼ cups Gruyère cheese.
Transfer the skillet to the upper rack and broil until the cheese is melted, bubbly, and browned in spots, 3 to 4 minutes. Garnish with the remaining 1 teaspoon thyme leaves and serve with crusty bread, if desired.

Make ahead: Bake the meatballs and caramelize the onions. After adding the flour and broth to the onions, remove from the heat (do not simmer to thicken or add vinegar yet). Add the meatballs to the onion mixture, cool, and refrigerate for up to 2 days. When ready to serve, transfer back to the skillet, and bring to a simmer. Continue with the recipe as directed.  Make ahead: Bake the meatballs and caramelize the onions. After adding the flour and broth to the onions, remove from the heat (do not simmer to thicken or add vinegar yet). Add the meatballs to the onion mixture, cool, and refrigerate for up to 2 days. When ready to serve, transfer back to the skillet, and bring to a simmer. Continue with the recipe as directed.
Storage: Leftovers can be refrigerated in an airtight container for up to 2 days.  Storage: Leftovers can be refrigerated in an airtight container for up to 2 days.