Move oven rack to middle position and preheat to 400 degrees F. Generously grease a 9x13-inch baking dish (or another oblong 3-quart baking dish) with butter, and set aside.
In a 10-inch non-stick skillet, add the olive oil and preheat the pan over medium heat. Add shallots, and cook, stirring often, until softened and golden, about 7-8 minutes.
Stir in Holland House Sherry Cooking Wine and cook until all the liquid is evaporated, about 3-5 minutes. Remove from heat.
Add the frozen hash browns to the prepared pan. Pour the melted butter over the potatoes, and add the salt, pepper, and caramelized shallots.
Use a spoon to give everything a good mix. Bake for 30 minutes, or until the potatoes are cooked through and some of the edges are beginning to brown. Remove the potatoes from the oven and reduce the temperature to 325 degrees F.
Sprinkle the cheese evenly over the potatoes followed by the ham.
In a large measuring cup or small bowl whisk together the eggs, milk, mustard powder, and dill. Vigorously whisk until fully combined and the eggs start to become frothy, about 1 minute.
Pour the egg mixture evenly over the potatoes, cheese, and ham.
Bake at 325 degrees for 35-40 minutes, or until the edges of the casserole are golden brown and the center of casserole doesn’t jiggle when you shake it.
Cool for 5 minutes before slicing and serving. Serve with additional grated Parmesan cheese and chopped dill (both optional).