Step 1To make the gum syrup: In a medium saucepan, combine the 2 cups sugar with one-half cup of water. Add the egg white and stir until combined. Cook the mixture over medium-high heat, stirring occasionally until the egg white has cooked and risen to the top, about 5 minutes. Strain it and any impurities floating to the surface, until you have a clear syrup. Strain the finished syrup through a cheesecloth-lined strainer into a nonreactive or glass container; you will have about 1 1/2 cups. Cool the gum syrup in an ice bath; it will keep for 1 week refrigerated.
Step 2Pare half of the lemon zest the same as you would an apple (all in one piece) so it will fit nicely into a wine glass. Slice one slice from the lemon, and juice 1 teaspoon of the remaining lemon. Reserve all.
Step 3Combine 1 teaspoon of the gum syrup, the bitters, brandy, curacao and lemon juice in a shaker with ice. Take the slice of lemon and run it around the rim of the wine glass. Dip the glass in the sugar, so that the sugar adheres to the rim. Fit the lemon peel into the prepared wine glass, then strain the cocktail into the glass. Serve immediately.