Step 1: To make the Vanilla Chai Syrup, combine water and granulated sugar in a small saucepan over medium heat. Stir until the sugar dissolves completely.
Step 2: Add the chai tea leaves or tea bags to the saucepan. Bring the mixture to a gentle simmer, then remove from heat. Let the chai steep for 5-7 minutes, or until desired strength is reached. Be careful not to over-steep, which can lead to bitterness.
Step 3: Strain the syrup through a fine-mesh sieve into a clean, heatproof jar or container to remove the tea leaves/bags. Discard the solids.
Step 4: Stir in the vanilla extract. Allow the syrup to cool completely to room temperature before using. Store any leftover syrup in an airtight container in the refrigerator for up to 1 week.
Step 5: To make the Vanilla Chai Old Fashioned, add 2 oz of Bourbon or Rye Whiskey, 0.5 oz of the cooled Vanilla Chai Syrup, and 2 dashes of Angostura bitters to a mixing glass.
Step 6: Fill the mixing glass with a generous amount of ice. Stir the mixture for about 30 seconds, until well-chilled and slightly diluted.
Step 7: Place a large ice cube in an Old Fashioned glass. Strain the cocktail from the mixing glass into the Old Fashioned glass.
Step 8: Garnish with a fresh orange peel. Twist the peel over the drink to express its oils before adding it to the glass.