Combine 2 cups water with the sugar, peppercorns, allspice and ginger in a small pot. Bring to a simmer over medium-high heat, stirring to dissolve the sugar. Simmer until slightly reduced and a bit syrupy, about 25 minutes. Remove from the heat, cool and then strain. You will have about 1 1/4 cups syrup.

Mix the ginger syrup and lime juice together. Fill each pint glass halfway with ice and add 2 to 4 tablespoons of ginger syrup, depending on how gingery you want it, to each glass. Pour a bottle of beer over the syrup, and then slowly pour a tablespoonful of dark rum over the top so it floats. Garnish each glass with a lime wedge.