Heat oven to 375 degrees F (190 degrees C).
Pick over mushrooms to discard leaves and twigs. Trim mushroom stems and brush them to remove grit. If very dirty, wash them by tossing in a large bowl of cold water, then lifting them out with your hands so grit falls to bottom of the bowl. Do not leave them to soak and absorb water. Drain them in a colander.
Peel and finely chop the shallots and garlic and push to the side of the chopping board. Chop the parsley, draw in shallots and garlic, and chop them briefly together. Stir them in a bowl with walnut oil. Cut any large mushrooms in 2 to 3 pieces and stir them all into the walnut mixture with salt and pepper.
Spread mushrooms in a baking dish, cover loosely with foil and bake in oven 20 to 25 minutes or until mushrooms are soft. Remove foil, stir, and continue cooking mushrooms until tender and any liquid has evaporated, 10 to15 minutes longer.