In a very large skillet, melt the stick of butter over moderately low heat. Add the sliced onions and a generous pinch of salt and cook, stirring occasionally, until the onions are soft and golden, about 40 minutes. Let the onions cool completely.
Preheat the oven to 350° and butter eight 5 1/2-inch gratin dishes (see Note). In a small bowl, whisk the flour with the baking powder and 1 teaspoon of salt. In a large bowl, beat the eggs with the heavy cream and grated cheese. Whisk in the dry ingredients until incorporated, then fold in the onions. Spoon the soufflé mixture into the prepared gratin dishes and bake for about 20 minutes, until the soufflés are set and golden on top. Serve right away.