Cut the eye of round roast in half crosswise (against the grain) so that it is easier to handle. Each piece should be about 2 inches thick. Using a skewer, poke the pieces all over so that the salt can penetrate the meat. Spread a thick layer of salt in a 9- by 13-inch roasting pan and place the meat on top. Coat all sides of both pieces with more salt so that the meat is barely visible. Cover and refrigerate for 2 days. (After 2 days, the salt will have drawn out a lot of liquid from the meat.)
Fill a large bowl with cold water. Drain the meat and rinse off the salt. Submerge the meat in the cold water for at least 1 hour or up to 3 hours. (This will draw out any excess salt.)
Remove the meat from the water and thoroughly dry each piece with paper towels, pressing down to remove as much moisture as possible. Wrap the meat completely in dry paper towels and place on a large, rimmed baking sheet. Place a second large baking sheet on top of the meat, then weigh down the top pan with a few 28-oz. cans of tomatoes or something similar in weight. Refrigerate at least 8 hours or overnight.
Find a place to hang the meat as it cures, preferably in a clean room that never exceeds 70°F, with some airflow. Next, uncover the meat and remove and discard the paper towels. The beef should be flat and slightly firm to the touch. With a skewer, pierce each piece about 1 inch from one end. Tie a piece of butcher’s twine in a knot on one end of the skewer and, leaving the other end of the twine long enough to hang the meat from the desired spot, thread it through the hole in the first piece of beef. Repeat with a second length of twine and the other piece of beef. Hang the meat up by the string and allow it to air-dry for 5–10 days, or until the pieces of beef feel as firm as a nearly-ripe avocado. (Alternatively, hang the meat in the refrigerator for 8 to 14 days. You may place a rimmed baking sheet underneath, though the meat should be dry from the cure and no longer dripping.)
Take the meat down, leaving the string in place, and transfer it to a large, clean baking sheet. Set aside.
In a medium bowl, mix together the fenugreek, paprika, allspice, black pepper, cayenne, cumin, and salt. In a small food processor, puree the garlic with ½ cup cold water. Add the garlic puree to the bowl of spices and mix thoroughly. Pour in an additional ½ cup cold water, or more as needed, until the mixture resembles thick pancake batter. Smear the spice mixture all over the meat in a thin (about ⅛ of an inch), even layer. Rehang the meat for 2–3 more days (3–5 days in the fridge), or until the spice mixture is firm and dry to the touch. At this point, the basturma is ready to eat. To serve, slice as thinly as possible against the grain with a sharp knife. Store the basturma wrapped tightly in plastic wrap in the refrigerator for up to 3 months.