How to Make It
Heat the canola oil in a very large skillet until shimmering. Add the brussels sprouts and season with salt and pepper, then cook over high heat without stirring until they are browned, about 2 minutes. Add the unsalted butter and brown sugar and cook over moderately high heat, stirring occasionally, until the brown sugar is melted. Add the maple syrup and cook, stirring occasionally, until the brussels sprouts are just crisp-tender, about 7 minutes. Stir in the cider vinegar. Add the chestnuts and walnut oil and cook until hot.
Using a slotted spoon, transfer the brussels sprouts and chestnuts to a bowl. Boil the cooking liquid over high heat until thickened slightly, about 2 minutes. Pour the sauce over the brussels sprouts and serve.