Preheat oven to 400 degrees.
Trim Romanesco leaves and base, but keep stalk mostly intact. Using a sharp knife, cut from the crown to the base to create ¾-inch slices. Brush both sides of the steaks with olive oil and season with sea salt and pepper. Toss the rest of the florets with a teaspoon of oil. Place all of the Romanesco onto a rimmed baking sheet and roast for 25 minutes, until they start browning.
Heat oil in a small saucepan until hot, but not smoking, about 2 minutes. Pour hot oil over scallion mixture and stir well. The scallions will begin to wilt. Let sit 5 minutes before adding remaining scallions. Stir in vinegar, garlic, sesame oil and sugar; season with sea salt. Let sit until flavors meld, 15 minutes. Taste and adjust seasonings.
Serve Romanesco steaks with scallion sauce spooned on top and sprinkled with breadcrumbs, if desired.