Add 1 cup sliced peaches, ½ cup light brown sugar, ½ cup water, ½ teaspoon vanilla extract, ¼ teaspoon cinnamon, and salt to a small saucepan. Bring to a simmer over medium heat, then reduce the heat and cook for 8–10 minutes.
Transfer to a blender and blend until smooth.
Taste and add a few drops of lemon juice if the syrup tastes flat.
Let cool, then store in a jar in the refrigerator for up to 1 week.