In a medium saucepan, add peaches, sugar, and water. Stir and bring to a gentle boil over medium heat.
Once bubbling, reduce heat and simmer for 10-15 minutes. Use a spoon or potato masher to crush the peaches and release their juices.
Place a fine mesh strainer over a bowl or jar. Pour the mixture through, pressing gently to extract every last drop of syrup. Discard the solids (or use them in yogurt or oatmeal!).
Add vanilla paste
Let the syrup cool completely before transferring it to a clean glass jar or bottle. Keep it sealed and chilled.