Rinse salmon with water; pat dry with paper towels.

Mix salt and sugar together in a bowl. Lay out a piece of plastic wrap. Pour half of the salt mixture onto the plastic wrap; lay salmon on top. Cover salmon with remaining salt mixture.

Fold plastic wrap around salmon until secure; wrap a second layer of plastic wrap around salmon. Transfer to a 9x9-inch baking pan; cover with an 8x8-inch baking pan. Place a heavy object onto the smaller baking pan to weigh salmon down. Cure in the refrigerator until salmon's surface becomes silky, about 48 hours.

Combine water and ice in a bowl. Mix water and 3 drops liquid smoke together in a bowl. Place salmon into liquid smoke mixture to rinse. Submerge into ice bath for 30 minutes. Repeat rinsing and submerging 2 more times, adding 3 drops of liquid smoke to the rinse water each time.

Dry salmon with paper towels. Cut with a sharp knife staring from the thin edge of the salmon and cutting toward the thick edge.