If using fresh mushrooms, clean off any lingering dirt with a pastry brush, then cut them into strips or dice. If using dried mushrooms, soak them for 20 minutes, or until soft, in lukewarm water, then drain them (reserving the liquid), squeeze them dry and chop them roughly.

Sauté the onion over gentle heat in butter, or in a mixture of equal parts butter and olive oil, until the onions have softened and are just starting to turn color. Raise the heat a bit, add the mushrooms and let them soak up the flavors of the onion for a few minutes, until they are also soft and any liquid has cooked off.

Add the rice and let it, too, soak up the flavors of the onion and mushroom. When the rice has turned a chalky white, add a splash of white wine and let that cook off.

Now, following the usual technique for making risotto, add the broth, one ladleful at a time, letting each ladleful cook off before adding the rest. The heat should be moderate, [so that it bubbles in a lively but not aggressive way.] The rice should take about 20 minutes total to cook.

When the rice is done, take if off heat and add the grated cheese and, if you like an even richer risotto, another nob of butter. Stir vigorously for about a minute, so that the rice becomes creamy and smooth.

Serve immediately.