Stir in 3 cups rice milk, brown sugar and 1/2 teaspoon cinnamon and bring to a lively simmer. Cook, stirring occasionally, for 10 minutes. Stir cornstarch and the remaining 1 tablespoon rice milk in a small bowl until smooth; add to the pudding. Continue cooking, stirring often, until the mixture is the consistency of porridge, about 10 minutes. Remove from the heat.