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

Beat the egg in a small bowl. Temper the egg by whisking in some of the hot rice, a tablespoon at a time until you have incorporated about 6 tablespoons. Stir the egg into the rice along with the vanilla and butter, and continue cooking over low heat for 1 to 2 minutes to thicken.