TO MAKE THE BEEF AND POTATOES:

Peel and slice the potatoes into a 3/8-inch-thick pieces. Put the slices into a pan with cold water to cover, add 1/2 teaspoon of the salt, bring the water to a boil, and simmer for 2 to 3 minutes or until the potatoes are tender. Drain and set the potatoes aside. Preheat the oven to 375 degrees F.

In a skillet over medium-high heat, heat the oil and saut? the onion until lightly golden brown, about 10 to 12 minutes. Stir in the flour with a wooden spoon and cook for 1 minute. Add the ground beef and break it up with the spoon. Saut? the beef for 10 minutes, scraping the bottom of the skillet with the wooden spoon. When the flour and beef are brown, pour in the beef broth, Worcestershire sauce, ketchup, the remaining salt, and the pepper. Bring to a boil, and simmer for 2 to 3 minutes, until thickened. Set aside while you make the sauce.

TO MAKE THE SAUCE:

Whisk the butter, flour, and milk together in a nonreactive saucepan. Heat to a boil, whisking constantly and vigorously, until the sauce is smooth and thickened. Simmer for 2 to 3 minutes, whisking frequently. Remove the sauce from the heat, and whisk in a 2/3 cup of the cheese and the egg yolk. Season with the salt and nutmeg.

TO ASSEMBLE THE PIE:

Spread the meat mixture in to a 9-x-9-inch casserole, then cover the meat with the sauce. Top the sauce with the potatoes, overlapping the slices to make a scalloped pattern. Cover with the remaining cheese and bake for 20 to 25 minutes, or until lightly brown. (For an extra-brown top, run the pie under a hot broiler.) Let the pie set at room temperature for 5 to 10 minutes before serving.