Lightly butter a round 3-quart glass or ceramic baking dish. Line the dish with parchment paper and brush the paper with some of the melted butter.
Arrange a single layer of overlapping potato and parsnip slices in an attractive pattern in the bottom of the prepared baking dish. Carefully layer 1/3 of the potato and parsnip slices on top.
Brush with some of the melted butter, sprinkle with half of the rosemary and season generously with salt and pepper. Repeat with the remaining parsnip and potato slices and rosemary to make 2 more layers, seasoning generously in between.
Pour the chicken stock over the vegetables. Cover with a sheet of parchment paper that is slightly larger than the baking dish. Set a heavy ovenproof skillet in the baking dish to weight down the cake and bake in the middle of the oven for 1 hour and 15 minutes or until the stock is absorbed and the vegetables are tender.
Preheat the broiler.
Remove the skillet and the parchment and broil the cake 8 inches from the heat for about 10 minutes, rotating the dish to evenly brown and crisp the vegetables.
Let stand for 15 minutes. Cover the baking dish with a flat cookie sheet and, using oven mitts, carefully invert the cake onto the cookie sheet.
Remove the baking dish and parchment paper.
Brush the cake with melted butter and season with salt.
Broil the cake 8 inches from the heat for about 12 minutes, rotating the cookie sheet as necessary to evenly brown and crisp the cake. Slide the potato and parsnip cake onto a large platter, cut into wedges and serve.
Make Ahead: The cake can be prepared through Step 4 up and refrigerated for 2 days. Reheat in the oven, then crisp the top under the broiler.
