Grate beets in the bowl of a food processor fitted with grater attachment. Place the grated beets in a large mixing bowl, then add Kosher salt, sugar, ground peppercorns, ground fennel seeds, and ground coriander seeds. Mix well.
On a medium rimmed baking sheet, lay out a double layer of plastic wrap, about twice the size of the salmon fillet. Lay about half of the fresh dill in the center of the plastic wrap, then sprinkle roughly half of the beet cure on top, in the shape of the salmon fillet. Place the salmon on top, then cover with the rest.
Transfer to a refrigerator, then place a couple of heavy items on top (cookbooks or a heavy skillet work well). Leave like this for 48 hours.
After remove the salmon from the fridge. Carefully unwrap it. Transfer the cured salmon to a cutting board, then thinly slice on an angle into paper thin strips. Cured salmon can be enjoyed immediately on bagels, english muffins, or cucumber slices.