Preheat the oven to 350°. Bake the sweet potatoes for 1 1/2 hours, or until tender. Raise the oven temperature to 425°.
Peel the sweet potatoes as soon as they are cool enough to handle; transfer to a bowl. Using a handheld electric mixer, beat the sweet potatoes with the butter until smooth. Beat in the cream, Gruyère, brown sugar and thyme; season with salt and pepper. Beat in the eggs one at a time, beating well after each addition.
Transfer the sweet potato puree to a buttered 8-by-11-inch baking dish and bake for 15 minutes. Reduce the oven temperature to 400° and bake for 30 minutes longer, or until the sweet potatoes are lightly puffed and browned. Let the sweet potato soufflé rest for 10 minutes before serving.