Preheat your oven to 400°F and lightly grease a 9x13 inch baking dish (or similar size for a crowd). While the oven heats, peel and slice the potatoes into thin 1/8-inch rounds—I find using a mandoline slicer speeds this up considerably. Mince the garlic cloves and finely dice the onion. Measure out the thyme, salt, pepper, cayenne, and nutmeg into a small bowl. Sift the arrowroot powder to remove any lumps before you need it, as this prevents lumpy sauce. Having everything prepped and ready makes the sauce preparation smooth and stress-free.
Arrange half of the sliced potatoes in an even layer across the bottom of your prepared baking dish, slightly overlapping the slices. This creates a sturdy foundation for the casserole and ensures even cooking throughout.
Melt the butter in a medium saucepan over medium heat. Add the minced onion and cook for 2 minutes, stirring occasionally, until it just begins to soften. Add the minced garlic, thyme, salt, pepper, cayenne, and nutmeg from Step 1, stirring constantly for about 30 seconds to bloom the spices and release their flavors into the butter. This short cooking time is crucial—it awakens the aromatics without burning them.
Pour the milk into the saucepan with the aromatic butter mixture and whisk in the sifted arrowroot powder from Step 1, making sure there are no lumps. Bring the mixture to a gentle simmer over medium heat, stirring frequently, and cook for 3-4 minutes until the sauce thickens noticeably. You'll see it coat the back of a spoon when it's ready. Remove from heat and stir in 3/4 cup of the cheddar cheese until completely melted and smooth. I prefer sharp cheddar like Tillamook because it adds more flavor complexity to balance the creamy potatoes.
Pour half of the cheese sauce from Step 4 evenly over the potato layer in the baking dish. Layer the remaining sliced potatoes on top in a similar overlapping pattern. Pour the rest of the sauce over this second potato layer, ensuring it seeps down between the slices. Sprinkle the remaining 1/2 cup of cheddar cheese over the top. Bake uncovered at 400°F for 40-45 minutes until the potatoes are fork-tender and the top is golden brown and bubbly around the edges. The dish is done when you can easily pierce the center with a fork—this signals the potatoes have softened throughout.
Let the scalloped potatoes rest for 5 minutes out of the oven before serving. This resting time allows the sauce to set slightly and makes portioning easier. Scoop portions directly from the baking dish, making sure each serving includes multiple layers of potato and creamy sauce.