- Preheat oven to 400 degrees. Using a mandolin, carefully slice sweet potatoes into ⅛-inch thick rounds.
- Butter the base of an 8- or 9-inch cast-iron or nonstick skillet. Arrange sweet potatoes in rings until bottom of skillet is covered. Sprinkle with thyme, salt, and pepper and brush with butter. Repeat until all potatoes are used.
- Butter one side of a piece of aluminum foil larger than the pan. Cover top of sweet potatoes with foil, buttered-side down, then place a slightly smaller pan on top of the foil.
- Cook on the stovetop over medium-high heat until potatoes are sizzling, then transfer skillet to oven (with second pan still on top). Cook for 20 minutes, then remove second pan and foil and bake until potatoes are easily pierced with a fork, 15 to 20 minutes more. Let rest 5 minutes, then invert pan onto a plate and serve.