Hakurei Gratin, Take Two!

As you may remember from a week or two ago, I burned my Hakurei Gratin. Now I know what I did wrong. When I cooked the gratin the first time around, I expected it to cook and look like a nicely layered scalloped potato dish fresh out of the oven. As a result, once I layered my turnip slices, I didn't touch them, so they burned in place! Now I know, once you remove the lid from this dish to cook off the excess liquids, jostle the pan continuously. At one point in the liquid cookoff process (about 15 or 20 minutes in, not in 5 or 10 minutes like the recipe says), the liquid will seem to thicken instantly. At that point, sprinkle the parmesan cheese on the turnips and take them off the heat. This is a delicious and very rich side dish. The Hakurei Gratin recipe (revised) is here:

Melt 1 tbsp butter in a non-stick 12-inch skillet (make sure you have a top to fit the pan). Wash one bunch of white hakurei turnips well, top and tail them, and slice them in 1/4-inch slices. Save the turnip greens for another recipe. You don't need to peel the turnips. Layer the slices in the pan. Sprinkle the sliced turnips with 1 tsp dry thyme, 3/4 tsp salt, 1/4 tsp freshly ground pepper, and 1-8-1/4 tsp cayenne pepper. Cook for 3 minutes over medium heat, then pour 1/2 cup heavy cream and 1/2 cup gluten-free chicken stock over the top. Cover and cook the turnips over medium heat for 20 minutes. The turnips will be completely cooked through, but there will be considerable liquid left in the pan. Remove the cover and cook to reduce the liquid. Jostle the pan frequently to help the liquid thicken. When most of the liquid has reduced (about 15 to 20 minutes), and the sauce is thickened, grate finely 1/2 cup fresh parmesan cheese evenly over the top. Watch closely as the cheese melts and make sure that the liquid does not entirely cook away. Serve the turnips hot. The recipe is supposed to serve 6, but maybe realistically it would only serve 4, once they discover that they love turnips!