6 ounces shiitake mushrooms, wiped clean
8 tablespoons (1 stick) unsalted butter
1 teaspoon kosher salt
2 cups (1 medium head) radicchio, finely shredded
2 1/2 cups heavy cream
1/2 cup (1 1/2 ounces) parmigiano-reggiano, freshly grated
1/2 cup (1 1/2 ounces) fontina, coarsely shredded
1/2 cup (3 ounces) gorgonzola, crumbled
2 teaspoons ricotta
6 leaves fresh sage, chopped
1 pound pasta shells
Preheat the oven to 400°F.
Bring 5 quarts of salted water to a boil in a stockpot.
Remove the stems from the mushrooms and reserve for another use. Slice the mushroom caps about 1/4-inch thick. Heat 6 tablespoons of butter in a large skillet; add the mushrooms and 1/4 teaspoon salt. Sauté over medium heat, stirring frequently, until they are cooked through, 3 to 5 minutes.
In a large mixing bowl, combine the mushrooms, radicchio, cream, cheeses, sage, and remaining salt.
Parboil the pasta shells for 4 minutes; drain and add to the ingredients in the mixing bowl. Toss to combine.
Pour the entire mixture into a 9-by-13-inch casserole dish. Dot with the remaining 2 tablespoons of butter, and bake until the radicchio has wilted and the shells are lightly browned in spots, about 25 to 30 minutes.