Whisk in flour, salt and pepper until well combined and all flour is incorporated. Whisk in milk and chicken stock. Bring to a gentle simmer, whisking often, then add broccoli and simmer for 5 minutes, stirring 2-3 times, until thickened.
Preheat oven to 350 degrees Fahrenheit while you assemble the lasagna. Lightly grease a 9x13" baking dish and coat the bottom with a thin layer of the sauce. Add ham to sauce, stir well, and season with additional salt and pepper to taste (do this after adding the ham as ham can add a lot of salt and you may not need any more seasoning). On top of sauce in dish, layer 4 overlapping noodles. Top noodles with half the meat sauce, then sprinkle with all the cheddar cheese. Do another layer with the remaining noodles, top with remaining sauce, and top everything with mozzarella cheese. Bake in preheated oven for 20-30 minutes, until heated through and cheese is melted and bubbly. Let stand for 5-10 minutes before cutting.
*To make ahead: fully prepare lasagna, then let stand at room temperature for 1 hour before wrapping with plastic wrap and foil. Refrigerate and use within 4-5 days, or freeze for longer storage. If frozen, let thaw overnight in refrigerator and bake according to directions, adding 10-20 minutes to heating time to ensure it is heated through.
Notes
This is delicious with your favourite additions, such as mushrooms, peppers, or spinach added to the sauce, or with chicken in place of the ham.
Recipe by Hidden Ponies at https://hiddenponies.com/2015/06/cheesy-ham-broccoli-lasagna/