Heat the oven. Set your oven to 425°F (220°C). Lightly grease a 9x13-inch baking dish with 1 teaspoon of olive oil.
Prep the cabbage. Remove the tough core, slice into thick shreds, and toss with 1 tablespoon olive oil, 1/2 teaspoon salt, and a few grinds of pepper.
Spread it evenly in the baking dish. You want some overlap so the top can crisp while the bottom steams.
Roast the cabbage first. Bake for 15 minutes to jump-start the tender-crisp texture. This prevents sogginess when you add the beef.
Brown the beef. While the cabbage roasts, heat a large skillet over medium-high.
Add the remaining olive oil, then the onion and a pinch of salt. Cook 3–4 minutes until softened. Add the garlic, stir for 30 seconds.
Season and simmer. Add the ground beef.
Cook, breaking it up, until browned with a few crispy bits, 5–7 minutes. Stir in smoked paprika, dried oregano, 1/2 teaspoon salt, black pepper, and Worcestershire. Pour in the beef broth, scraping up the browned bits.
Simmer 2–3 minutes until saucy but not watery. Taste and adjust seasoning.
Mix the sauce. In a small bowl, combine mayonnaise, ketchup, mustard, pickle juice, sugar, and paprika. Stir until smooth.
It should be tangy, a little sweet, and pourable. Thin with a teaspoon of water if needed.
Layer it up. Pull the cabbage from the oven. Spoon the beef mixture evenly over the cabbage.
Drizzle about half the burger sauce on top. Sprinkle with chopped pickles if using, then top with shredded cheese.
Bake to finish. Return the dish to the oven for 10–12 minutes, until the cheese melts and the cabbage edges look golden and crisp. If you want extra color, broil for 1–2 minutes, watching closely.
Top and serve. Let it rest 5 minutes.
Scatter green onions over the top. Serve with the remaining sauce on the side. Cut into squares or scoop with a spatula.