Preheat the oven to 325°F.

Grease a very large sauté pan and soft-scramble the eggs over medium-low heat. Season with salt to taste. Remove from the heat and set aside.

Make the gravy: Cook the sausage in large skillet over medium heat for 5 to 6 minutes, until thoroughly heated, stirring frequently. Gradually add the cream cheese and broth; cook until the mixture comes to a soft simmer and thickens, stirring constantly until smooth. Reduce the heat to medium-low and simmer for 2 minutes, stirring constantly. Season to taste with salt. Set aside.

In a 3-quart baking dish, assemble the lasagna: Start with a thin layer of gravy, followed by the first layer of “noodles” (thin-shaved ham), then a layer of soft-scrambled eggs, another layer of gravy, ¼ cup of the mozzarella, and ¼ cup of the Parmesan. Repeat the layers (gravy, “noodles,” scrambled eggs, gravy, cheeses).

Top with a final layer of “noodles” and a little more cheese. Bake for 25 to 35 minutes, until the cheese, is melted.