Place butter in a saucepan and heat gently. Add spring onions, mustard, parsley, tomato paste, tarragon vinegar, wine and season with salt and pepper. Add the crushed garlic clove and cook on a gentle heat for 2 minutes.
Dry sole and season with salt, cayenne pepper, chives and parsley and spread with a little melted butter. Place 1 fish fillet on top of the other, forming a sandwich, and lay in a well-buttered oven-proof dish. Pour over sauce and place in a preheated 350 degree oven for 20 minutes. Place clarified butter in a frypan, add the mushrooms and a squeeze of lemon juice and season with salt and pepper. Remove the fish from the oven and pour sauce into a pan. Add a little of the sauce to the egg yolk and then combine with the rest of the sauce. Heat gently until sauce thickens. Drain the mushrooms and add to the sauce. Mix the bread crumbs with the wine, the remaining lemon juice and grated cheese. Coat the fish with the thickened sauce and then cover with the bread crumb mixture. Place under the broiler until golden, about 3 1/2 minutes. Dust with paprika and serve.