Chop the carrots into tiny pieces, then add to a saucepan with the water. Bring the water to a boil over medium high heat, then reduce and add the brown sugar. Stir until sugar is dissolved and carrots are mostly fork tender, about 5-10 minutes.
Transfer all ingredients to a high speed blender. Pulse until smooth.
Strain the mixture, then stir in the ground cinnamon, pumpkin spice, orange zest, and grated ginger.
Store in a glass container in the fridge up to 4-5 days.
For the Cinnamon Maple Cold Foam:
Add all ingredients in a small bowl. Use a hand held milk frother to whisk until thick and foamy.
To Assemble the Latte:
Fill a glass with ice. Add 1-2 tablespoons of the Brown Sugar Carrot Cake Syrup, then the whole milk, then the espresso, and lastly top with the cold foam.