Heat broiler to high. Drizzle peach halves with honey and broil for 8-10 minutes until soft and charred. Remove and let cool on the counter about 5 minutes. This will make more than what you need for one cocktail. You can also omit the broiling process and just use the peaches as they are.
Pick the leaves off the rosemary sprigs. Muddle in the bottom of a cocktail shaker with one whole peach (2 halves), 1-2 tsp additional honey (optional), and lemon juice. Pour in bourbon and cider vinegar. Add ice and shake. Strain over ice in a glass. Top with sparkling water and garnish with fresh peach slices and a rosemary sprig.