Cook the pasta according to package directions. While the pasta cooks prepare the rest of the recipe.

In a non-stick skillet, melt the butter over medium-high heat. Place the steak in the pan and cook it on one side for 3 to four minutes. Turn the steak and cook it on the other side for another 3 to 4 minutes. Remove the steak from the pan and let it rest on a cutting board for a couple of minutes. Thinly slice the steak against the grain.

Beat the eggs in a large bowl. Add the cheese, basil, and salt and stir to combine. When the pasta is ready, drain it and place it in the bowl with the eggs. Toss the pasta with the eggs and cheese for a minute or until the pasta is evenly coated in the sauce (the heat from the pasta will cook the eggs). Add the sliced steak and toss a few more times. Divide the pasta between two bowls and top each serving with 1 tablespoon of grated Parmesan and a few pinches of ground black pepper.