Coarsely grind allspice and peppercorns in spice mill or with mortar and pestle; add spices and orange zest to rum and let infuse at least 2 days. Strain into a clean bottle or a glass jar.
DO AHEAD: Rum can be infused 3 weeks ahead. Store in a dark, dry place.
Combine lime juice and 4 ounces spiced rum in a cocktail shaker; fill with ice. Shake until outside is frosty, about 30 seconds. Strain into highball glasses filled with ice, top off with ginger beer, and garnish with lime wedges.
