Brown the mushrooms: Set a 10-inch skillet with a lid over medium heat and let it warm for about 1 minute.

Add the olive oil to the skillet and swirl it to coat the bottom.

Put the chopped onion into the skillet with a small pinch of the salt. Cook for 2 to 3 minutes, stirring often, until the onion looks softened.

Add the sliced mushrooms to the skillet and spread them into an even layer.

Sprinkle the mushrooms with 1/2 teaspoon of the salt and the black pepper.

Cook the mushrooms for 5 to 6 minutes, stirring once or twice, until they give off their liquid and then start to brown at the edges.

Transfer the mushroom mixture from the skillet to a plate and keep the skillet on the stove.

Cook the polenta: Pour the water and milk into the same skillet and raise the heat to medium-high. Bring the liquid to a gentle boil.

Slowly pour the instant polenta into the skillet while whisking the liquid the whole time so lumps do not form.

Turn the heat down to low and cook the polenta for 3 to 4 minutes, whisking often, until it is thickened but still loose enough to settle back into an even layer.

Stir 1/2 cup of the Parmesan into the polenta until it melts in. Taste the polenta and add more salt if it needs it.

Stir half of the mushrooms back into the polenta and spread the mixture evenly across the skillet.