Preheat oven to 400 degrees. Grease a 9x13 inch baking dish with butter or non-stick cooking spray and set aside.
FOR THE CHEESE SAUCE:
Melt the butter in a large skillet over medium-high heat. Add the garlic and cook for one minute, stirring constantly.
Whisk the flour into the butter and garlic mixture, whisking constantly for 2 minutes.
Gradually whisk in the milk until combined and season with salt, pepper, and paprika.
Bring the mixture to a simmer then remove from the heat and stir in the cheddar, parmesan, and chopped broccoli.
FOR THE POTATOES:
Wash the potatoes and peel off all of the skin.
Use a mandoline, sharp chef's knife, or food processor to slice the potatoes into ⅛ inch slices.
Layer half of the potatoes in the prepared baking dish and pour over half of the broccoli cheddar sauce.
Top the sauce with the remaining potatoes, and remaining sauce.
Cover the dish tightly with aluminum foil and bake for 30 minutes.
Remove the foil from the pan, sprinkle on the remaining cheese, return the potatoes to the oven and cook for an additional 25-30 minutes until potatoes are cooked through and the top is golden brown.
NOTE: The broccoli in this recipe is OPTIONAL if you would like to leave it out for regular scalloped potatoes. Make as directed, just omit the broccoli.NOTE: You can add 2 Cups of diced or cubed ham to make this into a full meal!