1) Preheat oven to 450F. In a large bowl toss sprouts with oil and season with salt and pepper.
2) Get a large cast iron frying pan super hot and in a single layer place sprouts cut side down until caramelized and browned. Add chestnuts and shallots and saute a couple minutes longer.
3) Put brussels sprouts in oven on top rack, roast for 10-20 minutes, stirring the sprouts about halfway through the cooking.
*Adjust the timing depending on the size of the sprouts and your particular oven.
5) Once brussels are done top with the compound butter and the parm. Adjust seasoning to taste.
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