Step 1Heat the oven to 350 degrees. Put the polenta in a 2-quart gratin dish, and stir in the water and 1 teaspoon salt. Bake for 45 minutes. Stir in 2 tablespoons butter and return the polenta to the oven for 15 more minutes.
Step 2Heat 2 tablespoons butter in a nonstick skillet over medium-high heat. Add the mushrooms and sprinkle with one-fourth teaspoon salt, or to taste. Cook, stirring frequently, until the mushrooms give up their moisture, about 5 minutes. Add the garlic and the rosemary and continue cooking until the mushrooms are dry, 3 to 4 more minutes.
Step 3When the polenta is done, taste and add more salt if necessary. Tear the soft Fontina slices into shreds and distribute them over the top of the polenta. Scatter the cooked mushrooms over the top and return the pan to the oven until the cheese has melted and begins to brown, about 5 minutes.