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.
In a soup pot over medium heat, melt butter. Add shallots and cook until soft. Sprinkle in flour and stir until blended. Slowly add milk and cream and stir until smooth. Add stock and brussels sprouts. Simmer for 10 minutes, uncovered. Do not boil. Taste, then season with salt and pepper. Garnish with bacon.