Preheat your oven to 400°F. While it heats, carefully slice your cabbage head into 1-inch thick rounds—these will be your burger bases. Lay the cabbage rounds on a baking sheet, lightly brush or drizzle them with oil, then season generously with salt and pepper on both sides. Place in the oven and roast for 10 minutes until they begin to soften and the edges start to caramelize slightly. This head start on the cabbage ensures it will be tender enough to hold the toppings without becoming mushy.
While the cabbage roasts, combine the ground beef, grated garlic, finely chopped yellow onion, chopped parsley, red chili flakes, smoked paprika, half of the shredded cheese, salt, and black pepper in a bowl. Mix gently with your hands just until combined—overmixing can make the beef tough. Divide into 4 equal portions and form into patties slightly smaller than your cabbage rounds so they fit neatly on top. I like to keep the patties on the thicker side rather than too thin, as they'll stay more juicy and flavorful during baking.
Remove the partially roasted cabbage from the oven. Spread a thin layer of tomato sauce on top of each cabbage round, then place a formed beef patty directly on top. Sprinkle the remaining shredded cheese over each patty to help bind everything together and create a melted cheese layer. Return to the 400°F oven and bake for 10-12 minutes until the beef is cooked through and the cheese is melted and beginning to brown. The red chili flakes in the meat add a subtle heat that really cuts through the richness of the cheese and beef.
Remove the baked cabbage burgers from the oven and let them rest for 1-2 minutes. Top each burger with a generous amount of chopped green onion for freshness and color. Transfer to serving plates and enjoy immediately while the cabbage is still tender and the cheese is warm and gooey.