In a medium bowl, stir together the espresso, 3 tablespoons brandy (or the 1 teaspoon vanilla) and the brown sugar; set aside. In a double boiler, beat together the egg yolks, 2/3 cup granulated sugar and 1/2 cup cream over simmering water until the mixture lightens in color and thickens, about 7 minutes. Transfer the insert to a larger bowl filled with ice water. Whisk until cold, about 5 minutes. Whisk in the mascarpone and the remaining 1 tablespoon brandy until smooth.
Dip half of the ladyfingers, one at a time, into the reserved espresso mixture and lay them flat in a single layer on the bottom of an 8-inch square baking dish. Spread half the mascarpone mixture on top. Repeat with the other half of the ladyfingers and the remaining mascarpone mixture. Refrigerate for 2 hours.
Using an electric mixer, beat the remaining 3/4 cup cream and 1 tablespoon granulated sugar on medium speed until stiff peaks form. Spread the whipped cream onto the chilled tiramisu and, using a small strainer, dust the whipped cream with the cocoa. Top with the chocolate curls. Cut into rectangles.