Fill a container large enough to hold the fish with water and salt the water generously. Gently place the fillet in the salted water and soak 10 minutes. Rinse well under cool running water and pat dry. Dump the salt water out of the container, rinse, and dry.
In a small bowl, mix the sea salt, sugar, and white pepper.
Place a layer of dill fronds in the container, large enough to make a bed under the fillet. Place the fish on top of the dill and cover the fillet, top and sides, with the salt-sugar cure.
Layer the top of the fish with more fresh dill, then cover the fillet with plastic wrap. Place a weight on top of the salmon (we used a loaf pan with a 28-ounce can of crushed tomatoes insidand place in the fridge overnight.
The next day, remove the plastic wrap and dill from the top of the fish, flip it over, replace the dill, and recover with fresh plastic wrap. Place the weight back on top of the salmon and put it back in the fridge overnight.
Remove the fish from the container, and remove all of the dill fronds. Rinse the salmon well under cool running water and pat dry. Proceed to carefully slice the salmon as thin as you can with the sharpest knife you have. Serve with rye or brown bread, quick pickled red onions, and aioli.