Heat a medium skillet over medium heat. Add butter to skillet and swirl to coat. Add onions, cover and cook for about 5 minutes. Uncover and continue to cook, stirring occasionally, until the onions reach a deep, golden brown color. This should take about 25 minutes, but will depend on how thinly the onion is sliced.

Transfer caramelized onions to a bowl and add water to skillet, scraping up any brown bits that may have formed. Bring water to rapid boil and gradually whisk in grits, making sure to prevent any clumps from forming.

Cover and reduce heat to medium-low. Cook until grits are thickened, no more than five minutes, adding more water if necessary. Remove from heat and stir in onion. Crumble in goat cheese and stir to combine. Add salt and pepper to taste. Serve immediately.