Mystery Sizzling Steak

Special tools: 4 sizzling (or fajita) plates with wooden bases.

1. To make the sides: Preheat the oven to 450°F (230°C; gas mark 8). Line a sheet pan with parchment paper and set aside.
2. In a medium bowl, toss the potato wedges and broccoli with the 1 tablespoon oil, 2 teaspoons each garlic and onion powders, and salt and pepper. Spread the potatoes and broccoli in a single layer on the prepared sheet pan. Bake for 7 minutes, then remove the pan from the oven and transfer the broccoli from the pan to a plate. Return the potatoes to the oven to cook for 23 minutes more, flipping them halfway through the baking time.
3. Meanwhile, make the hamburg steak: Heat a medium skillet (with a lid) over medium heat, then add ½ tablespoon of the oil. Once hot, add the onions and reduce the heat to medium-low. Cook, stirring occasionally, for 12 to 15 minutes, or until caramelized in color. Add the garlic to the onions and cook for 2 minutes. Stir in the pinch of the salt, then remove from the heat and let cool to room temperature.
4. In a large bowl, combine the ground beef, 3 teaspoons garlic powder, 2 teaspoons onion powder, smoked paprika, remaining ¾ teaspoon salt, and pepper to taste, and cooled onion-garlic mixture. Mix until well combined and sticky. (You may test the flavor by frying a small piece of the mixture and adjusting the seasonings as you see fit.) Form the mixture into 4 patties.
5. Add the remaining ½ tablespoon oil to the same skillet that the onions and garlic were cooked in and heat over medium heat. Add the hamburg patties and cook for 3 minutes per side, or until browned, then cover with the lid and cook for another 7 minutes, or until desired doneness (for medium, cook to an internal temperature of 155°F, or 69°C). Remove the patties from the pan and place on a paper towel-lined plate. Preheat the sizzling plates.
6. To make the red wine sauce: Add the butter and ½ tablespoon oil to the same pan that the hamburg patties were cooked in. Once the butter is melted, add the flour and stir until it forms a paste. Add the red wine and whisk until there are no lumps and the liquid makes a soft sizzle sound to indicate that the alcohol has evaporated. Add the beef stock, Dijon mustard, and salt and pepper, then cook for 2 minutes while stirring to combine. Transfer to a gravy boat.
7. To serve: Place the heated sizzling plates on their bases, then place a hamburg steak in the center of each plate with some roasted broccoli and potatoes at the right of it. Drizzle the meat with the red wine sauce.