Preheat the oven to 425 degrees. Line a baking sheet with parchment paper.

Slice 1-inch off the top of the cabbage. Slice the cabbage into 4 to 5 half-inch thick steaks and place them on the baking sheet. Top with 3 tbsp olive oil, kosher salt, and pepper. Roast the cabbage for about 20 minutes.

While the cabbage is cooking, melt 2 tbsp of butter in a skillet over medium heat. Add the sliced onions, kosher salt, and pepper. Cook for about 10 minutes, then pour in Guinness. Continue cooking until the onions are caramelized for about 10 more minutes. Remove from heat and set aside.

In a large mixing bowl, combine ground beef, kosher salt, pepper, and 1 tbsp olive oil. Form the mixture into burger patties.

Remove the cabbage from the oven and place a burger patty on top of each cabbage steak. Gently press to create a smash burger type topping. Return the baking sheet to the oven and cook for about 8 minutes.

Remove the baking sheet again and top the burgers with sliced cheese. Return the sheet pan to the oven to melt the cheese.

To serve, place the cabbage burgers on a platter. Top with Guinness onions and ketchup.