In a saucepan on medium heat, add in the olive oil and shallots. Cook until the shallots have softened and cooked down, about 2-3 minutes.
Add in the rest of the ingredients, except the arrowroot powder. Cook on medium heat till the blueberries soften, about 5 minutes.
Now add in the arrowroot powder and mix until the chutney thickens. Remove from the heat and take out the cinnamon stick. Let cool completely. Pour into an airtight container/gifting jar and store in the fridge. Enjoy!