Preheat the oven to 425 degrees F. Lightly spray a 12-cup muffin tin with cooking spray and set aside.
Melt the butter in a microwave or small saucepan over medium-low heat. Set aside.
Slice the russets and sweet potatoes 1/16-inch thick using a mandoline and place in a bowl. Toss the potato slices with the butter, herbs, garlic, 1 1/2 teaspoons salt and a few grinds of pepper until the potatoes are evenly coated. Layer the potatoes evenly in the prepared muffin tin, stacking them one on top of the other until they are about 1 inch above the top of each muffin cup. Bake until the edges of the potatoes are golden and crispy, about 25 minutes.
Let cool 5 minutes, then run a small offset spatula or butter knife around the edge of each stack to help them release. Transfer to a serving platter, sprinkle with Parmesan and serve immediately.
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