Make the basil syrup: Bring 1 cup water, the sugar, peppercorns and allspice berries to a simmer in a medium saucepan over medium heat. Cook, stirring, until the sugar dissolves, then continue to simmer until slightly reduced, 3 to 5 minutes. Remove from the heat and stir in the 1 cup basil. Let cool, then strain into a liquid measuring cup. Refrigerate at least 1 hour. (You should have about 1 cup syrup, enough for 8 cocktails.)
For each drink: Muddle the lime wedges and 2 basil leaves in a shaker with 3/4 ounce of the basil syrup. Add the light rum, fill with ice and shake well. Strain into a tall glass filled with ice and top with the ginger beer. Float the dark rum on top by pouring it over the back of a spoon. Garnish with a lime wedge.