Sear and braise the lamb chops. While the lamb is braising, peel and chop the potatoes and parsnips, and cook them until tender. Blanch the broccolini. Make the thyme oil, and mash with the drained potatoes and parsnips. Refrigerate each dish separately.
Reheat the lamb, covered, in a low-temperature oven, and rewarm the potatoes over low heat. Saute the broccolini. Make the clafouti batter, and put the dessert in the oven as you sit down to eat.
Just Before Dessert
Whisk the heavy cream to soft peaks, and dust the clafouti with confectioners' sugar.