In a heavy-bottomed pot or Dutch oven, melt the butter and olive oil over medium heat. Add all the sliced onions, stir to coat, and cover. Cook for 30 minutes, stirring occasionally.
Remove the lid, reduce heat to low, and add 1/2 teaspoon fine salt. Continue cooking 30–45 minutes, stirring every 10 minutes until the onions are deep golden brown and jammy.
Deglaze the pan with ¼ cup dry sherry (or white wine), scraping up any browned bits. Simmer until almost evaporated.
Reserve ½ cup of the onions for the meatballs.
Sprinkle the remaining onions with flour and tomato paste, stirring constantly for 3–4 minutes until lightly browned and fragrant.
Stir in Worcestershire sauce, beef stock, Better Than Bouillon (if using), thyme, and black pepper.
Simmer uncovered for 25–30 minutes to develop flavor and thicken slightly. Remove thyme stems.
Stir in vinegar at the end to brighten the flavor. Keep warm on low heat.
Make the Meatballs
Preheat oven to 400°F (204ºC).
In a large mixing bowl, combine milk, egg, Pecorino, salt, pepper, parsley, garlic, and bread. Mash into a soft paste (panade) and let rest for 5 minutes to fully absorb.
Add ground beef (and pork, if using) along with the ½ cup chopped caramelized onions.
Using your hands, gently mix just until combined — do not overwork the meat.
Form into 2-ounce meatballs (about golf-ball size) and arrange on a parchment-lined baking sheet.
Bake for 20 minutes, or until cooked through (internal temperature 160°F).
Assemble
Transfer the baked meatballs into the warm onion sauce.
Simmer gently for 10 minutes to let the flavors meld.
Spoon meatballs and sauce into an oven-safe skillet or baking dish.
Top generously with Gruyère (or Gruyère-mozzarella blend).
Broil for 2–3 minutes, just until bubbly and golden brown.
Garnish with chopped parsley or green onions before serving.
Notes
Parmesan Rind Magic: Add a Parmesan rind to the sauce while simmering for 20 minutes, then remove before serving. It infuses the sauce with nutty depth.
Flavor Boost: The splash of vinegar or Dijon mustard at the end cuts through the richness perfectly.
Serving Idea: These are fantastic over creamy mashed potatoes, buttered noodles, or toasted baguette rounds — just like a deconstructed bowl of French onion soup.