Add the water, carrots, brown sugar, pecans, granulated sugar, cinnamon sticks, and nutmeg to a medium saucepan and stir over medium heat.
Bring the mixture to a simmer, and simmer for 10 minutes, stirring occasionally. After the 10 minutes, remove from heat and allow to cool at room temperature for 15 minutes.
Strain the solids from the syrup, discarding the solids and reserving the syrup. Stir the extracts into the styrup, then transfer to a mason jar or syrup bottle and store in the fridge for up to 2 weeks.