Toast the nuts on a baking sheet in a 350°F oven, stirring occasionally, until very fragrant and the skins are deep brown and cracked, about 15 minutes. Wrap the nuts in a clean dishtowel (one you don’t mind staining); let steam for at least 5 minutes. Vigorously rub the nuts against one another in the towel to scrape off the skins (you won’t get them all; aim for about half). Chop the nuts coarsely.

Heat a 12-inch skillet over medium-high heat. When the pan is hot, add the oil and butter. As soon as the butter melts, add the Brussels sprouts and spread evenly around the pan. Sprinkle with salt and cook without disturbing until browned on the first side, about 3 minutes. Continue to cook, stirring the sprouts occasionally, until they’re well browned all over, another 5 to 8 minutes. Add 1/4 cup water, cover partially, and cook until tender, another 4 to 5 minutes (if the water evaporates completely during cooking, add more, 2 Tbs. at a time). Don’t overcook; the sprouts shouldn’t be mushy. Add the nuts. Season to taste with the lemon juice, salt, and pepper. Serve immediately or keep warm for up to 20 minutes.