Pan-fry the bacon over medium-low heat for about 5 minutes, until some of the fat is rendered but the bacon is still soft. Add the onion and continue cooking on low heat for about 8 minutes until the onions are soft and barely golden. Drain the bacon and onion on paper towel and pat off any extra grease. Toast the bread until it is dark golden brown but not burned. Cut into 1-inch (2.5-cm) cubes.
In a large saucepan or stockpot, heat the stock and add the bacon and onion mixture, bread, mustard, and bay leaf. Simmer, covered, for 15 minutes. Remove the bay leaf and pour in the milk. Purée in batches in a food processor. Add salt and pepper to taste.
Heat and serve in large cups with a parsley sprig as garnish.
For a more unusual presentation, froth 1 cup (240 mL) of the soup in a blender or mixer and gently spoon a bit of it on top of each cup.