Add the olives, rosemary, orange peel, and garlic to a clean Weck jar or other airtight glass jar. Add the Champagne vinegar, kosher salt, filtered water, and dry vermouth. Seal the jar and gently shake until the salt has dissolved and everything is well combined. Make sure the olives are fully submerged in the brine.
Refrigerate for at least 24 hours before using. After 24 hours, give the brine a taste and decide if you'd like to continue infusing.
Once the brine tastes how you like it, remove the rosemary, orange peel, and garlic. Keep the olives submerged in the brine and store refrigerated.