Preheat the oven to 450°F. Line a sheet pan with foil.
To prepare the cauliflower, remove the leaves and all but 1 inch of stem from the head. Place the head stem-side down on the cutting board. With a heavy, sharp knife, slice through the middle of the head to create two equal halves.
Drizzle the cauliflower on all sides with 2 tablespoons of the olive oil and arrange cut-side down on the sheet pan. Season with a few pinches of salt and twists of pepper.
Roast until golden brown, about 30 minutes. Flip the cauliflower and continue cooking for 15 minutes.
Meanwhile, set a medium saucepan over medium heat. Add ¼ cup water and 1 teaspoon black pepper and bring to a simmer. Add the butter and whisk to combine. Remove from the heat and whisk in the pecorino and remaining 2 tablespoons olive oil.
Top the cauliflower with the cheese sauce and serve.