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Core and cut 1 medium green cabbage into ¼-inch-thick shreds (10 to 11 cups); you can also shave it on a mandoline instead.
Place 1 teaspoon whole black peppercorns in a large skillet, preferably nonstick. Cook over medium heat, shaking the pan occasionally, until fragrant and you hear the peppercorns start to crackle or roll around the pan on their own, about 3 minutes. Transfer to a bowl.
Heat 1 tablespoon unsalted butter and 1 tablespoon olive oil in the same skillet over medium heat until the butter is melted. Add the cabbage and sprinkle with ½ teaspoon kosher salt, and stir as best you can to coat the cabbage in the oil (the skillet will be full).
Cover and cook for 10 minutes, stirring halfway through. Meanwhile, finely grate 2 ounces Pecorino Romano cheese (about ¾ cup), or measure out scant ⅔ cup store-bought grated. Reserve about 2 tablespoons of the cheese for garnish. Coarsely crush the peppercorns with a mortar and pestle or under a heavy pan on a cutting board, or coarsely grind in a spice grinder.
Uncover the cabbage and continue to cook, stirring occasionally, until the cabbage is very soft, 5 to 8 minutes more. Turn off the heat. Sprinkle with the cheese and black pepper, and toss to coat. Garnish with the reserved 2 tablespoons cheese and serve with lemon wedges if desired.