Combine gin and peppercorns, then let stand 15 minutes.
Stir together 1/2 tsp finely ground pepper and 1/2 tsp salt on a plate. Wet rim of 1 Martini glass with your fingertip and dip in salt mixture, rotating glass to coat rim. Repeat with 2 more glasses.
Strain gin through a fine-mesh sieve into a 16-oz cocktail shaker three-fourths full of ice. Add vermouth and bitters and stir 15 seconds. Strain into Martini glasses.
Cooks’ note: We’ve also got a web-exclusive recipe using the leftover Angostura bitters.