Step 1 Cook the onions, lightly salted, in one-fourth cup butter over a very low heat, stirring occasionally, for about 1 hour, keeping them covered for the first 40 minutes. If the heat is low enough and the saucepan of a heavy material, there will be no problem of coloration -- they should begin to caramelize lightly toward the end of an hour's time, at which point the flame may be turned up slightly and they should be stirred regularly until the entire mass is of a uniformly rich caramel color. Should there be signs of coloration too soon, the flame should be lowered even more, or the heat may be dispersed by separating the pan from the flame with an asbestos pad.
Step 2 Spread slices of bread thickly with the onions, arrange a layer in the bottom of the casserole, sprinkle over a thick layer of cheese, and repeat the process, packing each layer gently and arranging the bread slices as well as possible to avoid empty spaces. The last layer should be sprinkled only with cheese, and the casserole should not be more than two-thirds full at this point.
Step 3Bring the salted water to a boil in the same pan in which the onions were cooked. When it comes to a boil, pour it slowly and very carefully, at one single point against the side of the casserole, permitting the bread to swell and the mass to rise about 1 inch, or until obviously just floating, but no more (if you fear an unsteady hand, carefully ease the tip of a funnel down the side of the casserole to the bottom and pour the boiling water into the funnel).
Step 4Cook on top of the stove, uncovered, over a very low heat, the surface maintaining a light, slow bubble for one-half hour. Add, as before, just enough boiling water to be certain that the body of the bread is submerged, sprinkle a bit more cheese over the surface (sprinkle over a teaspoon of Cognac now, if you like), shave about 1 tablespoon butter in paper-thin sheets from a firm cold block of butter, distributing them over the surface and transfer the casserole to a medium oven (325 to 350 degrees) for 1 hour, raising or lowering the temperature, if necessary, after about 40 minutes' time, depending on how the gratin is developing. The soup should be covered with a richly colored crust of gratin and should be served out with a large spoon onto preheated plates.