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Melt 1 tablespoon of the butter in an 8-inch nonstick skillet over medium-low heat. Pour in 1/3 of the egg batter, cover the pan, and cook until the edges of the frittata brown slightly and the top is firm and not runny, 5 to 7 minutes. Transfer the frittata to a plate to cool. Repeat this step until you have 3 small frittatas.
Top the beef with the frittata. Roll the 2 together and secure with twine, making sure not to tighten too much, otherwise the twine will break through the beef, or push the frittata out of the roll. Repeat with the remaining beef and frittatas.
Heat the olive oil in a large skillet over medium-high heat, add the garlic and cook until it starts browning, 2 to 3 minutes. Add the rolls, searing the meat evenly all over by rolling them in the pan for 4 to 5 minutes.
Transfer the rolls to a cutting board to rest for 5 minutes. Slice 1/4-inch thick and serve with a drizzle of the pan juices.