In a medium saucepan over medium heat, combine the oil, wine, garlic and chiles. Add the artichokes and bring to a boil. Cook, partially covered, about 5 minutes.
Add the fava beans, peas and scallions. Cook 3 minutes more, lower the heat and stir in the escarole, basil, mint and salt to taste. Let simmer partially covered until the artichokes are tender, about 5 minutes.
Meanwhile, poach the eggs. Bring about 3 inches of water to a boil in a large saucepan. Add the vinegar to the water and reduce the heat to low. Crack each egg into a small ramekin and gently place the eggs in the simmering water, spacing them out so the whites do not touch.
Simmer until the egg whites are set, but the yolks are still runny, 3 to 4 minutes. Using a slotted spoon, gently remove the eggs from the water and place on a paper towel-lined plate to drain.
Serve the Scafata warm, topped with a poached egg and the Pecorino Romano cheese.
This recipe was provided by a professional chef or restaurant and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.