In a saucepan, combine vegetable stock and half & half; season with salt and pepper.
Bring to a simmer over medium-high heat.
Add polenta and water allow to reduce heat to a low simmer. Stir occasionally until combined and thickened, about 20 minutes.
Add butter and parmesan; stir to combine (if polenta becomes too thick, add more broth or half & half).
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