Combine 2 Tablespoons water and cornstarch in a small dish and set aside.
In a medium saucepan, bring water, sugar or honey, and blueberries to a boil. Stir occasionally. Reduce heat and simmer for about 10 minutes.
Add water+starch mixture and mix to combine. Turn off heat, let it sit for 5 minutes to thicken.
For a smooth syrup, transfer the mixture to a blender and blend until smooth.
Store in an airtight container or jar in the refrigerator for one to two weeks. Take out a few minutes before serving at room temperature or warm in the microwave.
