Place the ground beef in a large bowl. Add the smoked paprika, garlic powder, 1 teaspoon salt, and ½ teaspoon pepper. Stir everything to combine.
Form the meat mixture into 4 equal patties approximately 1 ½ – 2 inches thick.
Heat a large, heavy-bottomed skillet over medium-high heat and add 1 tablespoon butter. When the butter begins to foam, add the beef patties. Cook until they are no longer pink and register 160°F on an instant-read thermometer. Transfer them to a platter or tray.
Melt 1 tablespoon butter in the skillet with the residual drippings from the beef. Add the onions and cook over medium-low heat until they are translucent.
Add the mushrooms and an additional 1 tablespoon of butter to the onions. Continue cooking until the mushrooms have released (and absorbed) all their liquid, have browned, and shrunk in size.
Stir in the Worcestershire sauce and season to taste with salt and pepper.
Sprinkle the flour over the mixture and stir to form a paste. Slowly stir in the broth (¼ cup at a time), adding more broth only after the previous amount has been incorporated.
Once all the broth has been added, increase the heat to medium-high and stir in the remaining 2 tablespoons of butter.
Add the beef patties to the skillet with the gravy and simmer them until the patties are heated through and the gravy has started to thicken, occasionally spooning the gravy over the patties to keep them moist.
Garnish everything with chopped parsley and serve.