Preheat the oven to 400 degrees F. Generously butter a 12-cup bundt pan (use all the butter; it may seem like a lot, but the potatoes need it to stick to the sides of the pan and to crisp up).
Thinly slice the potatoes on a mandoline (they need to be thin enough to easily bend when folded). Starting on the bottom of the pan lay the potatoes in a slightly overlapping formation, sticking to the butter, until the entire pan is covered in one layer of potatoes.
Stir together the heavy cream, Parmesan, garlic, rosemary, scallions, 2 teaspoons salt and a few grinds of black pepper in a large bowl. Toss the remaining potatoes in the cream mixture until well coated.
Using a quarter of the potatoes, layer them in a circular formation, slightly overlapping in the bottom of the pan. Top with 8 pieces of the Cheddar in a slightly overlapping circle. Repeat two more times. Top with the remaining quarter of the potatoes so that all of the cheese is covered. Bake until the potatoes are a dark golden brown, crispy on top and a paring knife can easily be inserted and removed into the center of the dome, about 1 hour 20 minutes. Let rest for 10 minutes. Run a small offset spatula around the edges of the pan to help loosen the potatoes from the side. Invert onto a serving platter. Serve immediately.
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