In a thick-walled stockpot, over medium heat, add the water, and both sugars and store for 5 minutes until combined and fully dissolved.
Once the mixture starts to boil, reduce heat and add in cinnamon sticks, cloves, and dry spices. Allow to simmer over low heat for 10 minutes.
Remove pan from heat and plan a large bowl in the sink. Use your cheesecloth to gently strain the ingredients like the cloves and cinnamon sticks. If you do not have cheesecloth, you a fine mesh strainer.
Return strained liquid to the pot, and stir in pumpkin, extract, and sweetened condensed milk.
Allow mixture to cook over medium heat for an additional 5 minutes. Pumpkin will dissolve and mixture will be of medium thickness.
Turn off heat and allow mixture to cool before adding it to sterilized, glass mason jars or glass storage bottles.
This pumpkin spice syrup is more of a sauce-like consistency, and will keep in the fridge for a tested one week--possibly more, but ours didn't last that long.