Preheat oven to 375 degrees F.
In a food processor add hazelnuts and pulse 4 times at 5-second intervals. Add panko to the hazelnuts and pulse again for 10 seconds. Season the sole with salt and pepper, to taste, and lightly dust the sole with flour, shaking off the excess. Dip the sole into egg whites coating entirely, shaking off excess, press into hazelnut breading. Refrigerate for 10 minutes or up to 24 hours. Heat a large saute pan on medium heat. Add 2 ounces canola oil and the sole. Cook for approximately 1 minute, checking carefully with a spatula to make sure they are golden brown. Flip and continue cooking for 1 minute longer and then transfer to sheet pan. Repeat the process with the remaining oil and sole.
Place the baking sheet in the preheated oven for 8 to 10 minutes (depending on thickness of fillet) or until fish is cooked through but still moist.
Cook the potatoes through in a 6-quart stock pot with 4 quarts of salted water for approximately 30 minutes. Drain potatoes well. Beat with an electric mixer on low speed. Add half-and-half, shallot puree and salt and pepper, to taste. Cover and keep warm.
Reduce the Marsala wine and shallots in a heavy bottom pan over medium-high heat and reduce to 1/2 cup. Add heavy cream and bring back to simmer. Whisk in the cornstarch and water mixture, also known as a slurry. Reduce heat to low, whisk occasionally for 1 minute longer. Remove from heat. Add softened butter, 1-ounce at a time, whisking until smooth. Season with salt, pepper, hot sauce and Worcestershire sauce. Serve immediately.
In a pot big enough to hold all the vegetables, bring salted water to a boil. Drop in vegetables and cook until al dente, approximately 2 minutes, drain well. Toss back in pot, season with salt and pepper and add butter, if using. Keep warm until ready to serve.
Divide potatoes among 6 to 8-inch plates, placing them in the center. Place the Menemsha sole on top. Top 1 corner of the sole with 2 ounces of Marsala Wine Buerre Blanc. Arrange the vegetables around the plate, garnish with chives.