Brussels sprouts aren't known for their vibrant flavour so keep the salt handy here, you may need it to bring them to life.Feel free to increase the cheese sauce quantity if you wish it to be more saucy - it's currently a thick coating sauce.
Preheat the oven to 200°C/180°C fan/390°F. Prepare the chestnuts by carefully cutting a cross into their hard shells. Once the oven is hot, place them on a baking tray, add the two garlic cloves and roast everything for 30 minutes, until the shells are opening and the garlic is soft.
Bring a saucepan of salted water to a boil. Once boiling, add the sprout halves and cook for 5 minutes until softened. Drain through a colander and leave to sit as you make the cheese sauce.
In a smaller saucepan, add the flour and butter. Set over medium heat, allow the butter to melt and stir to combine into a paste. Cook for 2 minutes while stirring then remove the pan from the heat and gradually add the milk, stirring with each addition. It will thicken so beat out any and all lumps then add more milk. Continue until all the milk is gone and you have a smooth, silky sauce.
Return the pan to the heat and bring to a boil to cook the flour. Stir as it cooks for around 5 minutes. Remove it from the heat again and add 40g of the cheddar, the chopped rosemary and mustard. Squeeze the roasted garlic out of their skins and puree the cloves with your knife. Add to the sauce, season with salt and pepper and stir everything to combine.
Peel the chestnuts of their shells and any crunchy skin clinging to the meat. Chop the chestnuts into small pieces and add 100g to the cheese sauce.
Season the Brussels sprouts with a little salt and add them to the sauce too. Stir everything together again and taste for seasoning.
Tip the Brussels sprouts mixture into a baking dish and smooth it all down flat. Sprinkle over the breadcrumbs and the remaining grated cheese. Cook in the oven for 30 minutes until the breadcrumbs are no longer powdery and the cheese has melted. If you want, grill the gratin for 5 minutes to crisp up the topping. Serve the gratin alongside your Christmas lunch!