Preheat the oven to 425˚F. Line a baking sheet with parchment paper.
Heat 4 tablespoons butter in a large ovenproof braiser or deep skillet over medium-low heat. Add the onions and season with ½ teaspoon salt and ¼ teaspoon pepper; stir. Cover and cook, stirring once, until the onions are softened and translucent, about 10 minutes.
Uncover, increase the heat to medium, and cook, stirring, until very soft and deeply golden, about 10 more minutes.
Add the wine, thyme, and garlic and cook, stirring, until the liquid evaporates and the onions are caramelized, about 5 more minutes. Remove half of the onions to a cutting board to cool slightly. Finely chop.
Combine the panko, milk, parsley, mustard, egg, chopped onions, and the remaining 1 teaspoon salt and ½ teaspoon pepper in a large bowl. Add the beef, pork, and 1 cup of the gruyère and use your hands to gently mix until combined.
Shape into 36 golf ball–sized meatballs (about 1½ tablespoons each) and arrange on the prepared baking sheet. Bake until golden and cooked through, about 15 minutes.