Puree the thawed blueberries in a food processor or bender. *If you are using fresh blueberries please see notes below.
Whisk the water, lemon juice and arrowroot powder in a medium saucepan then add the blueberry puree.
Bring mixture to a boil slowly over medium heat, stirring frequently then simmer until it thickens, approximately 25 minutes. You will know when it is done when you draw a rubber spatula through the center and it creates a hole that will stay open for a few seconds and then fill back in. Once this happens remove from the heat.
Return mixture to the blender and process for a few seconds or use a hand blender if you have one directly in the saucepan.
Let it cool before you store it. As it cools, it will continue to thicken. If your butter becomes to thick, add a little water. You can also return it to the stove and cook it longer if you want a thicker butter.
*If you are using fresh blueberries add them to the saucepan directly along with the water, lemon juice and arrowroot powder and heat it for 5 minutes to soften the blueberries. Place mixture in your blender or food processor then return to the stove and follow step 3 and 4 above.