Drain all ingredients from the ice water and dry well with a kitchen towel. Place in a bowl and add the parsley, lemon juice, sugar and olive oil. Season well with kosher salt and freshly ground pepper. Mix to combine.
Blend all ingredients in a blender until smooth.
Heat a large heavy skillet over high heat with just enough oil to coat the pan. Pat the tuna steaks dry and season heavily with kosher salt and freshly ground pepper of salt.
When the oil starts to shimmer and just starts to smoke, place the tuna in the skillet and sear for 1 minute on each side for a rare. Cook longer for a more done tuna steak.
Slice with a very sharp knife to the desired thickness and serve with the slaw and aioli. Sprinkle the tuna with a little more sea salt for garnish.