Preheat oven to 400° F. Stand Romanesco on its stem and cut it from top to bottom into 1- to l½-inch thick slabs. You should get 3 or 4 intact pieces. Don't worry about the rounded outer edges that may crumble or any small florets that break away in large pieces, just scoot those to one side of the cutting board along with any nice-looking leaves; you'll use everything. Cut the loose bits into ½-inch pieces and season them and the Romanesco steaks with salt.
Heat a 10- or 12-inch cast-iron skillet over medium-high heat. Drizzle 2 tablespoons oil into the skillet and slip Romanesco steaks into pan-you might have to puzzle them together, but make sure they don't overlap. Work in batches if needed. Cook until Romanesco is dark brown on the underside, about 6 minutes. Turn over and drizzle a bit more oil over the second side and into the empty areas of the pan. Scatter the chopped pieces of Romanesco into the spaces between the steaks and toss gently to lightly coat them with oil (add more if needed).
Transfer pan to oven and roast until a cake tester inserted into stem slips through without much effort, 15 to 18 minutes. Steaks should be firm enough to still hold together without being crunchy.
Use a spatula to transfer steaks to a large plate or platter. Return pan with loose piece of Romanesco to medium-high heat. Add butter, hazelnuts, and garlic and cook, stirring, until everything is toasted and crisp around edge , about 4 minutes. Add vinegar and parsley and qt1ickly stir up any browned bits. Spoon this mixture over the steaks, season with flaky salt, and serve with lemon wedges for squeezing over.