Put the cornmeal and salt in a large heavy-bottomed pot and slowly whisk in the water. Bring the mixture to a boil over medium-high heat and then adjust the heat so the polenta just barely simmers when covered. Be careful, because the polenta will spit like lava, and it’s just about as hot!
Cook over gentle heat, stirring often with a long spoon or stiff silicone spatula, making sure to scrape the bottom of the pot and into the corners. Continue to cook until the cornmeal has fully expanded and doesn’t feel at all crunchy when you take a bite and the polenta pulls away from the sides of the pan, anywhere from 45 minutes to 3 hours, depending on your polenta.
Stir in the butter and cheese, if using. Taste, and adjust with more salt if needed.
Pour the cooked—but still fluid—polenta onto an oil-rubbed half sheet pan or 9- by 13-inch (23- by 33-cm) baking dish. You want the polenta sticks to be about 1/2 inch (1.25 cm) thick, so choose a pan that suits the amount of polenta you have.
Let the polenta cool and firm up, about 25 minutes. When completely set, flip it out onto a cutting board and cut into strips the size of fish sticks, or whatever shape you like.