Chop the carrots into small pieces, then add to a saucepan with the water, brown sugar, and spices. Bring the water to a boil over medium high heat. Stir until sugar is dissolved and carrots are mostly fork tender, about 5-10 minutes.
Strain the mixture and store in a glass container in the fridge up to 4-5 days.
Maple Cold Foam:
Add all ingredients in a small bowl. Use a hand held milk frother to whisk until thick and foamy.
Latte:
Fill a glass with ice. Add 1-2 tablespoons of Carrot Cake Syrup, then the milk, espresso, and top with the cold foam.