1. Combine vodka, coffee liqueur, cold‑brew concentrate, syrup, and water in a bottle or pitcher and chill until very cold (at least 2 hours). The added water mimics shake dilution for consistent strength.
2. For each cocktail, add 4 oz of the cold batch to a shaker with ice and shake hard for 15–20 seconds to build a thick foam.
3. Strain into a chilled coupe and garnish with three coffee beans. Keep the batch refrigerated up to 5 days.