Trim the Brussels sprouts of any discolored outer leaves and cut an “x” in their bases before cooking. Boil or steam them whole until just tender.
Melt butter in soup kettle. Saute shallots until soft. Sprinkle in flour and stir until blended. Slowly add milk and cream and stir until smooth. Add stock and Brussels sprouts. Simmer 10 minutes, uncovered. Do not boil. Season with salt and pepper. Garnish with crumbled bacon or chopped parsley.