When the butter and oil are bubbling in the skillet, add the onions and sauté over moderate heat for about 10 minutes, rolling the onions about so they will brown as evenly as possible. Be careful not to break their skins. You cannot expect to brown them uniformly.

Then either braise them as follows:

Pour in the liquid, season to taste, and add the herb bouquet. Cover and simmer slowly for 40 to 50 minutes until the onions are perfectly tender but retain their shape, and the liquid has evaporated. Remove herb bouquet. Serve them as they are, or follow one of the suggestions at the end of the recipe.

Or bake them as follows:

Transfer the onions and their sautéing fat to a shallow baking dish or casserole just large enough to hold them in one layer. Set uncovered in upper third of a preheated 350-degree oven for 40 to 50 minutes, turning them over once or twice. They should be very tender, retain their shape, and be a nice golden brown. Remove herb bouquet.

The onions may be cooked hours in advance, and reheated before serving.