Place a rack in the center of your oven and preheat to 375 degrees F. Coat a 9x13 inch casserole dish with nonstick spray and set aside.

In a medium pot or skillet with high sides, melt the butter over medium-low heat. Add the onion. Cook for 8 to 10 minutes, stirring often, until translucent. Adjust the heat as needed so the onion softens but does not brown. Stir in the garlic and cook just until fragrant, about 1 minute more.

Turn off the heat. Stir in the milk, broth, 1 teaspoon of the salt, and the black pepper. Set aside.

Peel the potatoes. With a mandoline slicer (this is the easiest!) or a sharp chef's knife, carefully cut the potatoes into VERY thin slices (about 1/8-inch thick; don’t cut larger or they may not cook through). Place the potato slices in a large bowl and sprinkle with the flour and remaining 1/2 teaspoon salt. With your hands, toss to combine

Spread one-third of the sliced potatoes in the bottom of the prepared dish. Spoon 1 cup of the milk-broth mixture over the top and sprinkle with 2/3 cup of the ham and one-third of the shredded cheddar cheese. Repeat layers twice more, so you have 3 layers each of potato, milk-broth, ham, and cheddar (you’ll end with the cheddar).

Lightly mist a large piece of aluminum foil with nonstick spray. Cover the dish with the foil, placing it spray-side down, and bake for 35 minutes. Uncover and bake for 25 additional minutes.

Remove the dish from the oven and sprinkle with the Parmesan cheese. Turn the oven to broil. Return the pan to the oven and let broil until the cheese is golden brown and bubbly, about 1 to 3 minutes (keep an eye on it!).

Sprinkle with the herbs. Allow the dish to stand at room temperature for 20 to 25 minutes to allow the milk mixture to set and thicken. Enjoy hot, with additional salt and pepper to taste (the amount of salt you need will vary based on the saltiness of your ham and broth).