1 cup coarsely grated sharp Cheddar (about 4 ounces)
1/2 cup fine fresh bread crumbs
1/4 teaspoon salt, or to taste
Preheat oven to 350 degrees.
Remove stems from mushrooms and chop stems. Melt butter. With a pastry brush gently brush mushroom caps all over with some melted butter. Arrange caps, stemmed sides up, on a large baking sheet.
Lightly toast walnuts and finely chop. Finely chop parsley. Finely chop onion and in a large heavy skillet saute with chopped stems in remaining butter over moderately high heat until mixture is softened. Remove skillet from heat and stir in remaining ingredients. Divide mixture among mushroom caps, mounding it slightly. Mushrooms may be stuffed 4 hours ahead and chilled, covered.
Bake mushrooms in middle of oven 20 minutes. Serve mushrooms warm.