Preheat the oven to 350°. In a pie plate or baking sheet, toast the hazelnuts until the skins blister, about 15 minutes. Transfer the nuts to a clean kitchen towel and let cool, then rub to remove the skins. If you don’t mind hazelnut skins, you don’t need to remove them. Coarsely chop the nuts.
In a large heavy skillet, heat the olive oil and butter over medium heat. When the oil is hot, but not smoking, add the capers (be careful since they will probably splatter!) Sauté the capers for about one minute, or until they start opening like little flowerbuds.
Add the Brussels sprouts and hazelnuts to the pan and stir to coat with the oil and caper mixture. Pour in the lemon juice and cook, stirring frequently, for about 5 minutes or until the sprouts are tender but still a little crisp.
Remove from the heat and add salt and pepper to taste. Serve immediately.