(The polenta takes about 10 minutes, but needs at least an hour to cool.)
Yield: 4 to 6 servings (depending upon what else is served)

You can make the polenta as much as a few days ahead of time. Wrap it in plastic wrap and store it in the refrigerator. It needs at least an hour to cool and firm up--preferably longer.
Butter is optional. It flavors the olive oil nicely, but is not essential. So if you prefer to keep this dish dairy-free, just skip it and slightly increase the olive oil.
The jalapeno adds a bit of heat. If you want to get a milder flavor, remove the seeds before you mince it. Wash your hands after handling this or any other hot pepper.

The Polenta

1 3/4 cups water
1 teaspoon salt
1 1/2 cups coarse cornmeal (polenta)
1 cup cold water

Pour 1 3/4 cups water into a medium-sized saucepan, add the salt, and bring to a boil. Meanwhile, place the polenta in a bowl with the cold water, and stir until it is completely moistened.
Turn heat under the boiling water down to a simmer, and spoon in the wet polenta. Stir with a wooden spoon, and cook over medium-low heat for about 5 to 8 minutes, or until very thick.
Turn the polenta out onto two dinner plates, spreading it into a thin circle all the way to the rims of the plates. Let it cool. It will become very firm.
Cut the polenta into cubes or dice, and proceed with the following recipe.

The Hash

2 tablespoons olive oil (and possibly more)
1 tablespoon butter (optional)
(Polenta pieces from above)
1 heaping cup minced onion
1 3-inch jalapeno, minced
2 teaspoons chili powder
1 teaspoon minced garlic
A dozen sliced cherry tomatoes, sliced in half (optional)
1 cup cooked black beans (canned OK), drained

Heat the oil in a large skillet (or two smaller ones) over medium heat. Add the butter and let it melt.
When the oil is very hot, add the polenta pieces in a single layer. Sauté them for a good 15 minutes, loosening and turning them about every five minutes with a metal spatula, to keep them from sticking. They will crumble somewhat, and that is desirable! (It makes a crisper result.) Don't move the pieces any more often than every five minutes, because they need a chance to "sit with the heat" in order to achieve texture.
When the polenta is looking golden in color, move it over to one side of the pan, add a little additional oil, if it seems necessary, and add the onion, jalapeno, and chili powder. Sauté these in the side of the pan, until they become soft (8 to 10 minutes). About 5 minutes into this step, add the garlic.
Mix the vegetables and polenta pieces together in the pan, still over the heat, adding the cherry tomatoes (if desired). Cook for another 5 minutes or so, then stir in the black beans until they're heated through. Be careful not to break the beans as you stir. The dish looks nicer if they remain whole.
Serve hot, with or without salsa.