Sauté the onions: Heat 1 tablespoon of oil in your cast iron skillet over medium heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, for 8–10 minutes, until the onions are soft and golden brown. (Photo tip: They should look caramelized, not just translucent — deep golden edges mean the sweetness has developed.) Add the minced garlic in the last minute and stir until fragrant. Transfer the onions to a plate.
Mix the patties: In a mixing bowl, combine the ground beef, breadcrumbs, egg, Worcestershire sauce, smoked paprika, dried thyme, ½ teaspoon salt, and ½ teaspoon black pepper. Mix gently with your hands until everything is just combined. Overmixing makes them tough. Form into 4 oval patties, about ½ inch thick.
Sear the patties: Add the remaining 1 tablespoon of oil to the same skillet over medium-high heat. Place the patties in the skillet, leaving space between them (work in two batches if needed). Sear for 3–4 minutes per side, until a deep brown crust forms. (Photo tip: The crust should be mahogany brown, not pale — that color is flavor.) Transfer the seared patties to a plate. They won't be cooked through yet — that's what the gravy simmer is for.
Build the gravy: Reduce the heat to medium. Pour about ½ cup of the beef broth into the hot skillet and scrape up all the browned bits from the bottom with a wooden spoon. This is called deglazing — it's the most important step for flavor.
Simmer the gravy: Add the remaining 1½ cups of broth and the cooked onions to the skillet. Stir to combine. Bring to a simmer, then let it cook for 2–3 minutes, until it thickens slightly.
Smother the patties: Return the seared patties to the skillet, nestling them into the gravy. Spoon some of the gravy over the tops. Cover the skillet, reduce the heat to low, and simmer for 10 minutes. The patties will cook through and the gravy will thicken beautifully.
Finish and serve: Uncover the skillet. If you're using the butter, stir it in now. Taste the gravy and adjust salt and pepper if needed. Serve the patties with plenty of gravy spooned over the top.