Crack the eggs into a large bowl. Pour in a tablespoon or two of cream and use a whisk to whip them together until frothy and evenly incorporated.
Cook the eggs in a large, non stick skillet over medium heat. Stir them occasionally to prevent sticking and break them up into rough chunks as they're cooked. Remove the cooked eggs from heat and set aside.
Spray a 9x13" baking dish with non stick cooking spray. Place 6 slices of french toast into the bottom of the dish-- in two rows of three each.
Drizzle syrup lightly over top. Spread half of the cooked eggs evenly out over top, followed by half of the diced ham, and finally 1/2 cup of the cheddar cheese.
Repeat the layer once more beginning again with the slices of french toast.
Spread the hash browns out evenly between several layers of paper towels, pressing them to remove any excess moisture. Top the casserole with the hash browns and spread them out evenly over top into a thin layer. Salt and pepper them to taste, before drizzling them with olive oil.
Bake at 350 degrees for 30-35 minutes. Remove the lasagna from the oven and sprinkle the remaining half cup of cheddar evenly out over top. Return the dish to the oven and bake for another 5 minutes or until the cheese is melted and the crust nicely crisped.
Let the dish rest for a minute or two before slicing and serving. Drizzle with additional syrup, if desired.