Gather the chestnuts and make a horizontal cut across the whole nut. This will give a larger surface area to be able to split open the skin and peel the nut, as opposed to the usual smaller cross shape. Make sure to cut through both the shell and the skin below, but try not to cut the nut itself (though it’s not the end of the world if you do).
Place the chestnuts into a bowl and cover with cold water until submerged. Set aside to soak for 1 hour.
In the meantime, prep the rest of the ingredients: trim the ends and then slice the brussels sprouts in half, finely chop the shallot and garlic, roughly chiffonade the sage.
Preheat the oven to 200°C. When the chestnuts have finished soaking, drain the water and dry them well. Arrange the nuts on a baking tray in a single layer, cut side up, and roast for 30-35 minutes. You’ll know they’re ready when they’re golden brown and tender, and the skin has pulled away from the cuts you made.
Remove the chestnuts from the oven, wrap them up in a towel and set aside for 10-15 minutes to steam and cool.
Peel the chestnuts when they are cool enough to handle but still quite hot – the cooler they are the harder they are to peel! Roughly break up the nuts into smaller pieces and set aside.
Start to cook the brussels sprouts by adding the oil and half the butter to a cast-iron skillet or heavy based frying pan (these will help in achieving a char). When hot, place the brussels sprouts into the oil-butter mixture, cut side down. Leave to cook, over medium heat and undisturbed, for 6-8 minutes or until they get a nice char on the cut side.
Now add the rest of the butter, shallots and garlic, sage, and season with salt and pepper. Mix well and leave to cook for a further 5-6 minutes, or until the brussels sprouts are tender on the outside and just starting to soften in the centre.
Add the chestnuts to the brussels sprouts, add the lemon zest from the whole lemon and then one good squeeze of lemon juice, or to your liking – but add a little at a time. Stir and cook for a further minute or two before serving.