Combine pumpkin puree and brown sugar in a small saucepan and whisk until smooth.

Add water to the saucepan and whisk until fully blended.

Mix ground cinnamon, nutmeg, cloves, and ginger in a small bowl, then whisk into the saucepan for 30 seconds to break up any clumps.

Place the saucepan over medium heat and bring the mixture to a gentle simmer, stirring occasionally.

Let the syrup simmer for 8 to 10 minutes, stirring every 2 minutes, until it thickens and coats the back of a spoon.

Remove the saucepan from the heat and let it cool for 2 to 3 minutes.

Stir in vanilla extract and a pinch of salt until fully incorporated.

If desired, strain the syrup through a fine-mesh strainer into a clean glass jar to remove any pumpkin particles.

Let the syrup cool completely to room temperature before sealing the jar with a lid to prevent condensation.

Store the syrup in the refrigerator for up to 3 to 4 weeks and stir well before each use; warm slightly in the microwave for 20 seconds before adding to cold coffee.