Juice one lime, reserving juice. Dice the lime shell.
Place Tuaca in bottom of shaker with mint leaves. Muddle leaves along with lime shell until the fresh mint flavor is released. Add simple syrup and rum along with cracked ice. Shake to break up the mint leaves.
Pour into tall mojito glass over more cracked ice. Top with Asti Spumante or your favorite sweet champagne. Stir and serve.