Though excellent with cold raw oysters, this lively sauce can also be drizzled onto crab cakes, or added to crab dip or oyster stew for a little extra zip.
Cut a 1-inch slit in side of pepper. Place in a small saucepan with carrots, onion, vinegar, sugar, and allspice. Bring to a boil, then remove from heat. Let cool completely, about 1 hour.
Divide solids equally among a few bottles; fill with vinegar mixture. Refrigerate up to 6 months. To serve, spoon vinegar mixture into oysters, or serve alongside.