Stir together vegetable broth, 1/2 cup water, oat milk, and salt in a saucepan over medium-high heat. Bring to a boil. Reduce heat to medium-low and sprinkle in polenta, stirring constantly. Continue stirring until polenta thickens, about 5 minutes.
Reduce temperature to low and cook, stirring often, for about 10 minutes. Add vegan cheese and butter. Stir until smooth. Add remaining water, if necessary, to keep consistency velvety and smooth. Pour polenta onto an oiled plate and let stand a few minutes before serving.
