For bechamel sauce: In a heavy sauce pan over moderately low heat melt butter. Whisk in flour and cook roux, whisking, 3 minutes. Whisk in milk and simmer sauce, stirring, about 8 minutes. In a bowl whisk eggs and add 1 cup sauce in a stream, whisking. Whisk egg mixture into remaining sauce and whisk in dill, nutmeg, and salt and pepper to taste. Keep bechamel warm, its surface covered with plastic wrap.
Preheat oven to 375 degrees F.
In a pot of boiling salted water cook penne until al dente. Rinse penne in colander and drain well.
In a bowl stir together pot roast meat, beef broth, and gravy. In a buttered shallow 2-quart baking dish spread half of pasta evenly and spread beef mixture evenly over it. Top evenly with remaining pasta and pour bechamel over pasta. Sprinkle pastitsio with cheese and bake in middle of oven until bechamel is set, about 40 minutes.
Recipe courtesy of Gourmet Magazine