Cut the bacon into slices and put into a pan over a medium heat. Dice the onion and once the fat starts to render from the bacon, add the onion to the pan. Cook, stirring regularly for 2-3 minutes.
Meanwhile peel the potatoes and dice. Take the outer layer and ends off the Brussel sprouts and cut in half. Add both to the pan, stir, then cover and reduce heat slightly.
Allow the vegetables to sweat for around 10min until the potato is tender to a knifepoint, stirring occasionally. Don't worry if things stick to the bottom of the pan and color a bit, it all adds to the flavor, just don't let them burn.
Add the stock, nutmeg and some salt and pepper to taste to the pan (bear in mind you have bacon in there so you won't need much salt). Cover and bring to a boil then simmer for around 10 minutes.
Meanwhile, put the bacon for the topping in a small skillet/frying pan and cook over a medium heat. Once the fat starts to render, add the chestnuts. Continue to cook until both are crispy, stirring now and then.
Remove the soup pan from the heat and puree the soup in a blender/with a stick/ immersion blender.
Serve the soup with the crispy bacon and chestnuts on top.