Rinse the potatoes and slice into ⅛" to ¼" slices. Leave them unpeeled. Lightly grease a 2 quart baking dish and layer the potatoes.
Preheat oven to 400 degrees Fahrenheit.
In a saucepan, melt butter over medium-high heat. Add flour and mix well. Whisk in milk and half & half slowly to mix with the flour. Add in all seasonings, 1 ½ cups of cheddar, and all of the Parmesan cheese. Cook until cheese is melted through, then pour over top of the potatoes.
Cover the dish with foil and bake for 60 minutes. Remove foil and bake an additional 15-20 minutes or until tender. In the last 5 minutes, sprinkle remaining ½ cup of cheddar cheese on top.