To make the crab mixture, set the crab aside in a strainer to drain liquid. In a mixing bowl, whisk the egg yolks, mayonnaise, mustard,Tabasco®, chives, tomatoes, tarragon, salt and nutmeg together. Add the crab to the ingredients in the mixing bowl, and fold with hands. Add the panko bread crumbs and mix well. Scoop 2-ounce balls of mixture onto a sheet pan and set aside. Wrap the crab balls in kataifi phyllo dough until enclosed and completely covered. Place on a sheet pan; cover and set inside the refrigerator.
To make the sauce, in a saucepan saute the shrimp, onion and garlic in the butter until lightly browned. Add the tomatoes and tomato paste, cook for 8 minutes. Deglaze with the white wine, and reduce until the wine is evaporated. Add the lobster base, Old Bay® seasoning, tarragon, thyme, heavy cream, and let it simmer for 30 minutes. Remove from heat and puree the mixture in a blender. Strain through a chinois, and reserve until ready to use.
To serve, place each kataifi-wrapped crab on a spoon and slowly immerse into a preheated fryer set at high heat until golden brown. Remove and drain on paper towel. Pour 2 ounces of the hot sauce in each martini glass. Place the fried lava crab in sauce and garnish with chopped chives.