In a heavy 5- to 6-quart kettle heat oil over moderate heat until hot but not smoking and cook onions with thyme and salt and pepper to taste, stirring occasionally, until golden, about 15 minutes. Reduce heat to moderately low and cook, stirring frequently to keep from scorching, until golden brown. Remove kettle from heat.
While onions are cooking, bring a large saucepan of salted water to a boil for potatoes. Peel potatoes and cut crosswise into 1/4-inch-thick slices. Add potatoes to boiling water and cook 5 minutes from time water returns to a boil. Drain potatoes well in a colander.
Preheat oven to 425°F. and lightly oil a 2- to 2 1/2-quart shallow baking dish.
Arrange half of potatoes, overlapping slightly, in dish and season generously with salt and pepper. Cover potatoes with onions, spreading evenly, and top with goat cheese. Arrange remaining potatoes, overlapping slightly, over cheese and season generously with salt and pepper. Dot gratin with butter.
Pour cream evenly over potatoes and bake 35 minutes, or until potatoes are tender and top is golden. Gratin may be made 1 day ahead and chilled, covered. Reheat gratin before serving.
Adapted from Gourmet, September 1995