Prepare the aromatics and meat: Peel and thinly slice the onion and mince the garlic. Divide the ground beef into four equal portions (about 113 g / 4 oz each). Gently form each portion into a 3/4- to 1-inch thick patty and make a shallow 1/2-inch wide indentation in the center of each patty with your thumb — this prevents the patties from puffing up as they cook and helps them stay flat for even contact with the pan.

Season the patties just before cooking: Sprinkle the patties on both sides with about 1 tsp kosher salt total and the black pepper and smoked paprika (distribute remaining salt evenly). Salting immediately before searing seasons the meat without drawing out excess moisture the way salting too far in advance can; the smoked paprika adds a subtle, smoky depth without needing smoke or bacon.

Caramelize the onions (low and slow for maximum sweetness): Heat 1 tbsp olive oil and 1 tbsp butter in a heavy skillet over medium-low. Add the sliced onions and a pinch of salt and cook, stirring every 2–3 minutes, for about 18–22 minutes until deep golden and soft. Lower heat and cook patiently — this slow process converts the onions’ starches into sugars, producing sweet, complex flavor that lifts the whole dish.

Add garlic and herbs to the onions: With the onions nearly done, push them to the pan edge, add the minced garlic and dried oregano to the cleared space and cook for about 30–45 seconds until fragrant, then stir into the onions. Cooking garlic briefly in hot fat mellows its raw bite and releases its aroma without burning (burned garlic becomes bitter). Remove the onion mixture to a bowl and set aside, leaving the fond (browned bits) in the pan.

Preheat the pan and sear the patties: Wipe the skillet clean or use a second heavy skillet and heat it over medium-high until shimmering. Add the optional 1 tsp oil and place the patties into the hot pan indentation-side up. Sear, undisturbed, for 3–4 minutes to build a deep brown crust (this Maillard reaction is where much of the savory flavor develops). Flip and sear the second side 3 minutes for medium; cook an additional 1–2 minutes if you prefer medium-well. For food safety, ground beef should reach 160°F (71°C); use an instant-read thermometer to confirm.

Finish with butter to build the pan jus: When the patties are nearly done, reduce heat to medium-low and add the remaining 1 tbsp butter to the pan. As it melts, tilt the pan and spoon the foaming butter over the patties for 30–60 seconds to enrich the surface. The butter emulsifies with pan drippings and helps create a glossy, flavorful jus to spoon over the steaks.

Rest the patties: Transfer the patties to a plate and tent loosely with foil for 5 minutes. Resting lets the muscle proteins relax and the juices redistribute, so the steak remains juicy when cut or bitten into.

Rewarm and glaze the onions: Return the onion mixture to the skillet for 1–2 minutes to rewarm and pick up any fond. Taste and adjust seasoning with a final pinch of salt and pepper. Reheating briefly brightens the onion flavors and allows them to soak up the pan’s savory browned bits.

Plate and serve: Place a rested hamburger steak on each plate, spoon a generous mound of caramelized onions over the top, and drizzle any remaining butter-jus from the skillet over the steaks. Serve with burger buns, mashed potatoes, roasted vegetables, or a simple green salad if desired. The contrast of crust, buttery sauce and sweet onions is what makes this humble ingredient feel special.

Storage and reheating: Leftover patties keep covered in the refrigerator for up to 3 days. Reheat gently in a skillet over low heat with a splash of water or a knob of butter and cover to avoid drying out. Do not microwave at high power — that tends to toughen ground meat.