Preheat the oven to 450 degrees F. Set out a 3 quart (9X13 inch) baking dish.
Shred both the cheeses, then mix them together. (Use block cheese and shred it yourself, because it melts better than pre-shredded cheese.)
In a medium bowl whisk the broth, sour cream, and corn starch together until very smooth. Then whisk in the thyme leaves, garlic powder, nutmeg, 2 teaspoons salt and 1/2 teaspoon cracked black pepper.
Use a mandolin slicer, or sharp knife, to slice the potatoes into even 1/8 – 1/16 inch rounds. Make them as consistent as possible.
Layer one-third of the potatoes in the bottom of the dish. (They do not need to be arranged in a certain way; random overlapping is fine.) Pour one-third of the cream mixture over the potatoes. Sprinkle with one-third of the cheese and half the chopped scallions.
Repeat with the second layer of potatoes, liquid, cheese, and the remaining scallions. Add one final layer of potatoes, liquid, and cheese.
Cover the pan tightly with foil and bake for 45 minutes. Then remove the foil and bake another 10-15 minutes, until the top is golden and bubbly around the edges, and the potatoes in the center are fork-tender.
Let the scalloped potatoes rest for 10 minutes before serving so the cheese sauce thickens a little.
Video
Notes
Cheese Swaps - Don't love swiss cheese? Try colby, muenster, gouda, or even pepper jack in its place. You can use any cheese you like in place of the swiss or cheddar, as long as it is a good melting cheese.