In a bowl, combine the grated beet, salt, sugar, horseradish, lemon zest, crushed spices, and vodka. Stir until you have a slushy, fragrant mixture that looks like a slightly chaotic beet salad.
Lay a large piece of plastic wrap on a baking dish or sheet tray. Spread half of the beet cure in the shape of your salmon. Place the salmon skin-side down on top. Cover the top of the fillet with the remaining beet mixture, pressing it gently into the flesh. Tuck dill sprigs around or on top, if using.
Wrap the salmon tightly in plastic wrap. Place a second tray or board on top of the fish and weigh it down with a few cans or a small cast-iron pan. This helps the cure penetrate evenly.
Refrigerate for 48–72 hours, flipping the salmon once a day. (48 hours for a softer cure, 72 for firmer and saltier.)
When ready, unwrap the salmon and scrape off the cure. Gently rinse under cold water and pat very dry with paper towels. Slice thinly on the bias using a sharp knife.
Notes
Don't skip the pin bones – run your fingers along the fillet and pull out any bones with tweezers.Wrap it tight and press it down – this keeps the cure in contact with the fish and helps it firm up nicely as it cures.Flip once a day – turning the salmon halfway through ensures an even cure and better texture throughout.Don't over-cure – 48–72 hours max. Any longer and it can get overly salty or dry.