Trim stems and remove any wilted outer leaves from fresh Brussels sprouts; wash. Cut any large Brussels sprouts in half lengthwise.
Fill a large Dutch oven* with water to a depth of 1 inch. Bring water to boiling. Place a steamer basket in the Dutch oven. Place Brussels sprouts in the steamer basket. Cover and steam for 10 minutes or until Brussels sprouts are tender. Remove Brussels sprouts from steamer basket and place in a large colander to drain.
Meanwhile, in a medium skillet cook shallot and walnuts in hot butter for 5 minutes or until shallot is tender and walnut is toasted. Stir in sour cream, thyme, and salt; heat through. Toss steamed Brussels sprouts with shallot mixture to serve. If desired, stir in milk, 1 tablespoon at a time, until it reaches desired consistency.