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Preheat the oven to 375°. Use a pastry brush to coat the inside of eight to ten 1-cup soufflé molds evenly with softened butter. Fill each mold with granulated sugar, the sugar sticks to the bottom and side of them.
Place a 1 quart saucepan half-filled with water over medium heat and bring it to a simmer. Make a double boiler by setting a large heatproof mixing bowl over the simmering water. Place the caramel-walnut base in the mixing bowl and heat until warm. If the base is too thick (having the consistency of peanut butter), you can add the rum to loosen it slightly. The base will be easier to incorporate into the warm meringue if they are each about the same temperature.
Pour the egg whites, meringue powder, and lemon juice into a medium-size mixing bowl and whisk to combine. Old egg whites whip better than fresh ones but adding meringue powder to fresh egg whites will produce the same result. The lemon juice will keep the egg whites from separating and having a crumbly texture.
While the base is heating, pour the water, sugar, and corn syrup into a 1-quart heavy-bottomed saucepan and place over medium-high heat. Insert a candy thermometer and cook the mixture until it reaches 250é, what is known as the soft ball stage. Remove the cooked sugar from the heat.
Use an electric mixer set on medium speed to whip the egg whites for about 5 seconds. Increase the mixer speed to medium-high and make an Italian meringue by pouring the hot sugar down the side of the mixing bowl into the whipping whites. Be careful not to pour the hot sugar directly onto the beaters, or it will splatter. I add the cooked sugar when I start to whip the meringue to give the meringue more strength and elasticity while making it heavier. This will help the soufflé hold up for 2 to 3 hours before being baked. Continue to whip the meringue until stiff and glossy, about 5 minutes.
Combine about one third of the meringue with the caramel walnut mixture, using a rubber spatula to gently fold them together. Fold the remaining meringue into the mixture. Remember to fold to the bottom of the bowl to evenly distribute the walnut mixture. Use a rubber spatula to fill the prepared soufflé molds, rounding the tops. Place the soufflés in the oven on the center rack and remove the top oven rack if necessary to allow enough room for them to rise. Bake until the soufflés have risen to about one and a half times their original height and start to brown on top, about 20 minutes. I prefer the center of the soufflé to be soft and a little wet. If you like a drier soufflé, bake it a few minutes longer. Serve immediately with a side of whipped cream or crème anglaise, if desired.