In a medium saucepan, whisk together all ingredients except vanilla. Bring to a boil over medium heat, then reduce heat to medium low, and simmer 10-15 minutes while gently smashing the apples against the pan with the back of a fork. Continue to simmer until mixture is reduced and coats the back of a spoon.
Turn off heat and let syrup cool completely. Strain though a fine-mesh sieve into a glass jar. Stir in vanilla extract. Store in refrigerator.
To Make the Cold Brew:
Fill a glass or glass jar with ice. Pour prepared Apple Brown Sugar Syrup over the ice. Pour coffee over. Pour milk on top.
