Remove any outer green leaves from the cauliflower and then cut it in half. Cut out the tough portions of the stem.
Now we're going to grate or "rice" the cauliflower. You can do this a few different ways: If you have a food processor, you can use the grater attachment OR the blade attachment. If you use the blade attachment, be careful not to blend it too long -- turn the machine off as soon as the cauliflower is in tiny pieces (the size of rice grains or bread crumbs). You can also use a hand held grater -- this takes longer and more muscle, but will do the job. Set the grated cauliflower aside.
Coat the bottom of a large sauté pan with olive oil and place it over medium high heat. Add the mushrooms and cook, stirring often, until golden, about 8 minutes. Sprinkle with a bit of salt and pepper and spoon them into a bowl. Set aside.
Turn the heat to medium and add 2 tablespoons of the butter. Once it's melted, add the onion and garlic and cook, stirring often until they're soft, about 5 minutes.
Now add the grated cauliflower and mix to be sure it's well coated with the onions, garlic and butter. Sauté for a few minutes and then add the stock and sherry. Mix, bring to a boil, and then turn the heat to low-medium, just high enough to keep it simmering. After about 5 minutes, turn the heat up a bit and, stirring frequently, cook until all but a tablespoon or so of the liquid has been absorbed, about another 5 minutes.
Add the mushrooms back into the pan. Then add the basil, cheese and remaining tablespoon of butter. Stir to blend and season to taste with salt end pepper.