1. Preheat oven to 425 degrees. To make the puffs, melt the butter in the water with salt and sugar over low heat. Remove from heat and beat in flour with a wooden spoon until completely mixed. Return to heat and stir vigorously for 2 to 3 minutes. Mixture will form a mass, and a film will form on bottom of pan. Remove from heat and, one by one, add eggs, beating vigorously after each addition.

2. Using a pastry tube with 1/2-inch opening, form puffs on a buttered baking sheet. Glaze each puff with the beaten egg and water, using a pastry brush. Smooth the top of each puff. Put in the oven for 20 minutes. Remove from oven and pierce each puff with a sharp knife (This allows the steam to escape so that the interior of the puff is not soggy). Return to the oven for 10 minutes more. Cool puffs on a rack. While cooling, prepare pastry cream.

3. To make the cream, beat the egg yolks, gradually adding the sugar, until mixture is thick and pale yellow. Beat in the flour. Add the hot milk in dribbles, reserving 1/2 cup for thinning. Return to pot in which milk was scalded, and stir mixture over high heat until it comes to a boil. It will become lumpy first and then will smooth out with vigorous stirring. Be careful not to scorch the bottom of the pot. The cream should be thick, but add milk if too thick to pipe.

4. Add the butter, one tablespoon at a time. Flavor with vanilla, cognac, and salt. Cool completely. Inject the pastry cream into the puffs with a 1/4-inch pastry tip.

5. To make the nougat, melt the sugar with the lemon juice in a heavy pot. Do not stir. Boil together until a thick amber syrup is formed. Stir in the almonds and spread the mixture on an oiled marble slab while warm. Cut with a sharp knife into a round for the base, and into small triangles for decoration, Keep nougat warm in a 250 degree oven. (It cannot be cut or shaped if it hardens.)

6. To make the caramel, bring the ingredients to a boil over high heat. Do not stir. Cover pan (allowing steam to dissolve any crystals that might form). Uncover pan and boil several more minutes, until syrup is amber. Reduce heat to keep syrup from hardening.

7. Dip the filled cream puffs, one by one, into the caramel syrup and arrange on the nougat base, forming a cone resembling a pyramid. The caramel holds the cream puffs together.

Note: Assemble the croquembouche the day of the party, as it cannot be refrigerated. However, the cream puffs, pastry, and nougat can be prepared in advance.