Preheat the oven to 375 degrees F. Line a 15”x10”x1” baking sheet with parchment paper so that the paper extends an inch or so higher than the sides; grease or spray the paper and set aside. (Tip: I fold the paper along the edges of the pan to make it conform better to the pan. The protruding edges will help when rolling later.)
In a mixing bowl, beat cream cheese and milk until smooth. (I’ve also done this by hand. In this case, mixing in a small amount of milk first will slowly break down the cream cheese and make it easier to incorporate. Small pieces of cream cheese that do not incorporate—aim for smaller than peas—are not a problem.)
Add the flour, Dijon, salt and several good grinds of the pepper mill; mix until combined. Beat or whisk in the eggs until well blended. (Prep ahead tip: at this point the egg mixture may be covered and refrigerated. I’ve refrigerated for about 5 hours but think overnight would be fine.)
Pour into the prepared pan, and bake for 20 minutes, or until the eggs are puffed and just set.
Remove from the oven. Sprinkle with 1½ cups of the cheese, and then lay the ham evenly over the surface and sprinkle with the green onions.
Using the parchment as an aid, roll up the short side, peeling the paper away while rolling. Sprinkle top of the roll with the remaining cheese, and bake for 3-4 minutes or until the cheese is melted. Sprinkle with some sliced green onions, if desired, and then slice and enjoy. The roll may be served warm or room temperature.