Preheat the broiler on high and position an oven rack directly (3-4 inches) below the heating element.
Sprinkle the Kosher salt, black pepper, garlic powder, onion powder, and smoked paprika on the meat. Work the spices gently and evenly into the meat.
Divide the seasoned meat into four 4-ounce portions and gently shape them into patties, 3.5 inches in diameter and ½ inch thick.
Arrange the patties in a 12-inch cast-iron skillet. Push down on the center of each patty to create a dimple. This will help the burgers stay flat as they cook.
Broil the burgers to medium, about 3 minutes per side (see notes below).
Turn the oven off, top each patty with sauteed onions and cheese, and return the pan to the still-warm oven for just a few seconds, until the cheese is melted. Serve immediately.
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Notes
The USDA recommends cooking ground meat to an internal temperature of 160°F.
A good alternative to smoked gouda is extra-sharp cheddar or smoked cheddar.
I use lean (85/15) ground beef. In my experience, a leaner mixture will result in dry hamburgers, so I don't recommend it.
You can use ¼ cup of finely diced onions and a tablespoon of fresh minced garlic instead of the powders.
To avoid dense burgers, try to handle the meat lightly during all steps of this recipe, including seasoning the meat and shaping the patties.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. Reheat them gently in the microwave at 50% power. Start with about 30 seconds per side per patty and see if they're heated through.
You can also freeze the completely cooled leftovers in freezer bags for up to three months. Thaw them overnight in the fridge and reheat them in the microwave.