Mark chestnuts with an X on flat side. Bring a pan of water to the boil over medium high-heat. Drop in the chestnuts and boil for about 6-8 minutes. Remove pan from heat.
Remove few chestnuts from the pan leaving the others in the water until ready to peel. Using a knife remove the shell and skin while chestnuts are still hot.
Put the peeled chestnuts in a pan with milk and enough water to completely cover them and simmer over medium heat for about 10-12 minutes until tender. Drain and set aside.
Remove any yellow leaves from the Brussels sprout, trim the roots and mark an X on the underside to cook evenly.
Melt the butter in a large frying pan. Add the onion and garlic and cook until softened. Add the Brussel Sprouts and water and cook covered over medium heat for about 8-10 minutes, stirring occasionally. Add more water if necessary.
Add the chestnuts and toss the mixture to combine and cook for a few minutes until the sprouts and chestnuts are heated through. Season with salt and pepper and serve hot as a holiday side dish.