Combine cooked brown rice, milk, blueberries, honey, and cinnamon in a small saucepan. Bring to a boil, then reduce heat to low; simmer for 20 minutes.

Beat egg in a small bowl. Whisk 6 tablespoons hot rice mixture, 1 tablespoon at a time, into egg to temper until incorporated. Stir tempered egg mixture, butter, and vanilla into rice mixture; continue cooking over low heat to thicken, 1 to 2 minutes.