If Using the Presoaking Method: Combine water with cornmeal in a large mixing bowl and let stand, covered, at room temperature overnight. When ready to cook, scrape soaked cornmeal and water into a large saucier or saucepan and set over high heat. Continue with step 3.

If Using the Standard Method: Add water, milk, or stock to a large 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 presoaked cornmeal and 50 minutes for dry cornmeal. Season with salt.

Stir in butter or olive oil, using either a spoon, a silicone spatula, or a whisk. Polenta will become glossy from the added fat, and should feel rich, creamy, and smooth. 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 liquid is fully incorporated and no lumps remain.

Serve right away with accompaniment of your choice, or continue with step 6 to sear or grill.

To Sear or Grill: Grease a rimmed quarter sheet pan with olive oil. Pour hot polenta into pan, then use a spatula to spread evenly. Place a sheet of parchment or plastic wrap against surface to further smooth and even surface. Wrap pan well in plastic, and refrigerate until completely chilled and set, at least 5 hours or up to overnight.

Using a thin spatula, loosen block of polenta. Invert onto a cutting board. Cut polenta into squares, rectangles, triangles, or circles, as you desire.

To sear, heat a large cast iron skillet over high heat. Coat bottom of skillet with oil, then, when shimmering, add polenta. Cook undisturbed until browned, crisp, and easily releases from skillet, about 3 minutes. Flip and repeat on second side. To grill, heat charcoal or gas grill over high heat. Clean and oil grates. Add polenta and cook undisturbed until browned, crisp, and easily releases from grill, about 3 minutes. Flip and repeat on second side.

Serve topped with accompaniments of your choice (such as gorgonzola dolce).