Bring the water to a boil over medium heat. Pour the cornmeal in slowly, whisking steadily.
Once all the cornmeal is added, turn the heat to low. Stir frequently until the polenta starts to thicken, about 5 min.
Put a tight-fitting lid on the pan and stir about every 5 minutes. When the polenta gets too thick to whisk, switch to a wooden spoon. The polenta is done when the texture is creamy and the individual grains are tender. How long this takes depends on how coarse the cornmeal is. Coarse grind will take longer. Albers was done in 30 minutes, probably less to be honest but I give it 30.
Remove the polenta from the heat. Stir in the butter and cheese. Then cover it and let sit for about 5 min to thicken. It should still be somewhat soft when you eat it.
This stiffens up in the fridge, but if you kind of chop it up, add a little water, and microwave it, it softens again.