If using the standard method, add water to a 3-quart saucier or saucepan and set over high heat. Sprinkle in cornmeal while whisking (water does not have to be boiling).
Bring to a boil, stirring frequently. Let boil, stirring frequently, until polenta thickens enough that it starts to spit. Lower heat immediately to prevent spitting and continue to cook, stirring frequently with a spoon or silicone spatula and scraping bottom to prevent scorching, until polenta becomes thick and pulls away from side of saucepan, about 30 minutes for pre-soaked cornmeal and 50 minutes for dry cornmeal. Season with salt.
Stir in butter or olive oil using either a spoon, silicon spatula, or whisk. If polenta forms lumps, beat vigorously with a stiff whisk to remove. If polenta becomes too firm or begins to set, add a small amount of water, stock, or milk, and beat in with a whisk until fully incorporate and no lumps remain.
Serve right away with accompaniment of your choice, or scrape into a vessel and chill until set, then cut into pieces for grilling, searing, or frying.
Add stock and wine to a large stock pot and bring to a boil. Whisk in cornmeal, whisking well to ensure there are no lumps.
Bring to a boil, stirring frequently. Reduce heat to a simmer and stir frequently with a wooden spoon, scraping the bottom to make sure it doesn't scorch. Simmer and stir until polenta thickens. Add butter, heavy cream and salt and pepper. Continue stirring until desired thickness is reached.
Serve with your favorite stew or roasted vegetables.