Wash clams thoroughly, discarding any opened shells; place in a stockpot. Add 4 cups water; cover and bring to a boil over medium-high heat. Cook 5 minutes or until shells open, discarding any unopened clams. Remove clams with a slotted spoon, and place in a large bowl. Cool. Remove clam meat from shell, reserving any juice. Coarsely chop clams, and set aside. Pour liquid through a wire-mesh strainer into a 4-cup liquid measuring cup, discarding solids. Reserve 3 cups liquid.
Cook bacon in a Dutch oven until crisp; remove bacon, reserving 2 tablespoons drippings in pan. Add onion and thyme, and sauté 5 minutes or until onion is tender. Add potatoes, 3 cups reserved clam liquid, half-and-half, salt, and pepper; bring to a boil. Cover, reduce heat, and simmer 7 minutes or until potatoes are tender. Stir in bacon, clams, parsley, and separated mushrooms; serve immediately. Garnish with fresh oyster mushrooms.