Preheat an oven to 450°. In a 12-inch ovenproof skillet, melt the butter, remove from the heat and set aside.
Mix together the thyme, salt, cayenne and nutmeg in a small bowl. Arrange ⅓ of the sunchokes, overlapping tightly, in bottom of skillet. Sprinkle with ⅓ of the thyme mixture. Repeat two more times for three layers total.
Return the skillet to medium heat and cook uncovered for 10 minutes, until underside of bottom layer starts to brown.
Add the cream, cover and cook 20–25 minutes, until the sunchokes are tender.
Sprinkle cheese over the top and place the skillet in the oven. Bake uncovered, 10–15 minutes or until golden and bubbling.
Remove from oven. Let stand 5 minutes, slice into wedges and serve.
Pair this dish with a nice, crisp Finger Lakes Chardonnay like this lightly oaked 2011 version from Wagner Vineyards.