Crush the peppercorns with the bottom of a small heavy skillet, the side of a chef’s knife, a spice grinder or a mortar and pestle. Combine the brown sugar, kosher salt and crushed peppercorns in a small bowl. Set aside.
Pat the salmon dry and lay skin side down in a 9x13 glass baking dish. Drizzle with the aquavit and rub it into the surface of the salmon with your fingers. Sprinkle the salmon with the salt, pepper and sugar mixture and rub to coat the surface evenly, making sure it is completely covered. Top with an even layer of chopped dill.
Tightly wrap the baking dish in plastic wrap. Place a cutting board, smaller baking dish or something else that is about the same size as the piece of salmon on top of the fish. Stack a few cans or jars of vegetables or beans on top to weigh the salmon down. Transfer everything to the refrigerator and let the salmon cure for 12 hours or overnight.
Take the salmon out of the refrigerator and remove the plastic wrap, cutting board and weights. Drizzle the top of the salmon with some of the accumulated juices from the bottom of the dish and pour off and discard any remaining juices at the bottom of the pan. Flip the salmon over so that it is now skin side up. Wrap with a new piece of plastic wrap and top again with the cutting board and weights. Place it back in the refrigerator for another 12 hours.
Repeat the process above one more time, flipping the salmon so that it is now skin side down again. Rewrap with fresh plastic wrap and replace the board and weights. Back to the refrigerator for 12 more hours.
Take the salmon out of the refrigerator (the total cure time should be about 36 hours) and remove the plastic wrap, cutting board and weights. Using a paper towel, wipe the dill and any remaining rub from the top of the salmon.
Transfer to a platter or cutting board and slice on the bias against the grain of the fish into very thin slices, leaving the skin behind. Serve with rye bread and/or crispbread, mustard dill sauce, lemon wedges and/ or dill sprigs.