In a medium saucepan, combine the blueberries, lemon juice, honey, and cinnamon.
Place the saucepan over medium heat and cook, stirring occasionally, until the blueberries release their juices and start to break down, about 5-7 minutes.
In a small bowl, mix the cornstarch with water to create a slurry. Slowly stir the slurry into the blueberry mixture.
Bring the mixture to a simmer and cook for another 2-3 minutes, stirring frequently, until it thickens to your desired consistency.
Remove from heat and stir in the vanilla extract.
Allow the compote to cool slightly before serving. It will thicken further as it cools.