To make the Pickled Onions: In a small bowl, combine red wine vinegar with 1/2 cup of cold tap water. Stir in salt, the sugar and the hot sauce. Add the sliced onions and let sit for at least one hour.
To make the Chicken Milanese: Set up a standard breading procedure in 3 wide deep plates. Fill 1 with flour, 1 with the beaten eggs, and 1 with the panko and grated Parmigiano. Season the chicken breasts with salt. Using one hand for dry things and 1 hand for wet things, take each piece of chicken through the breading procedure: dredge lightly in the flour, then the egg wash and then through the bread crumbs. Lay the breaded chicken on a sheet tray and refrigerate for at least 1 hour.
Pour olive oil into a large saute pan until it reaches a thickness of about a half an inch - better a little more rather than a little less. Bring to a medium-high heat and add butter. Test the oil by flicking flour or bread crumbs into the oil. If it doesn't sizzle-WAIT! When the oil is hot, test it again by dipping the edge of a piece of chicken into the oil, the oil should gently sizzle. Cook the chicken in the oil in batches on both sides until it is a lovely golden brown color and is crispy, about 4 to 5 minutes. Do not crowd the pan or the chicken will become very greasy and soggy. When the chicken comes out of the oil lay it on paper towels to drain off the excess oil and sprinkle with salt. You can keep the chicken in a low oven to keep it warm while the rest of the chicken is cooking.
To make the Escarole Salad: Combine the pecorino, hazelnuts and parsley in the food processor and pulse until they are coarsely chopped. Toss together the escarole, hazelnut mixture and some of the pickled red onions and dress with some of the pickling liquid and olive oil. Season with salt.
Place chicken on each serving plate and top with the escarole salad.