Prepare the Brussels sprouts, by steaming until tender - about 7-14 minutes depending upon the size of the sprouts.
While the Brussels sprouts are cooking start the hollandaise sauce. To make the hollandaise sauce: place the vinegar in a small saucepan with the chopped shallot, 4 peppercorns and the thyme and bay leaf. Simmer gently, uncovered, to reduce to about 2 tablespoons Strain and set aside.
Have 1 oz of the butter cut into small cubes and chilled in the ice-making compartment of the refrigerator.
Beat the egg yolks with a balloon whisk or hand-held electric beater until creamy in the top of a double boiler or in a heatproof bowl that will fit snugly over a saucepan. Gradually beat in 1 tbsp iced water and a pinch of salt.
Add half the chilled butter pieces and set the double boiler top or bowl over gently simmering water; beating continuously as the mixture gradually heats and the butter melts and combines with the egg yolks, adding the reduced vinegar a little at a time as you beat.
When this mixture starts to thicken noticeably, remove from the heat immediately, add the remaining chilled butter and continue beating.
Once this has melted and combined with the egg mixture, beat in the melted butter, starting by adding a few drops and then gradually increasing this to a thin trickle. The sauce should become light and thick.
Add a little more salt and freshly ground white pepper if wished and then stir in lemon juice to taste.