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 softened and translucent, about 10 minutes.
Uncover, increase heat to medium, and cook until very soft and deeply golden, about 10 more minutes.
Add the wine, thyme, and garlic and cook until liquid evaporates and onions are caramelized, about 5 more minutes. Remove half of the onions to cool slightly and finely chop.
Combine panko, milk, parsley, mustard, egg, chopped onions, remaining 1 teaspoon salt, and ½ teaspoon pepper in a large bowl.
Add the beef, pork, and 1 cup of gruyère and mix gently 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.