Heat oven to 400°F.
Using a food processor, pulse a few pieces of sour dough or wheat bread several times until finely crumbled.
Drain beets. Coarsely chop 1/2 cup beets.
Trim stems flat and remove gills from mushroom caps using a spoon. Place caps, rounded side down, on foil-lined baking sheet; season with salt and pepper.
In medium bowl, combine chopped beets, bread crumbs, green onions and walnuts. Spoon mixture into caps and top with goat cheese.
Bake 12 to 15 minutes or until heated through and mushrooms are tender.