Preheat oven to 400°F. Cut an X in the flat side of each chestnut and place on a baking sheet. Roast for 20 to 25 minutes or until shells pop open. Cool slightly and wrap in a clean kitchen towel to keep them warm. (This also makes them easier to peel.). Snap off the shells and peel away any of the inner skin that sticks to the nuts. Halve or quarter the nuts or chop coarsely, if you like.

To prepare Brussels sprouts: Wash and remove any damaged outer leaves. Cut off and discard the woody ends. Slice the sprouts thinly using a mandolin or food processor. To slice by hand, slice each sprout in half, place the cut side down on a cutting board, and then slice as thinly as possible.

Toss the sliced Brussels sprouts, shredded kale, and lemon juice together in a large salad bowl. Add chopped chestnuts, cheese, olive oil, salt, and pepper. Toss gently together and serve.