How to Make It
Heat 1 tablespoon of the oil in a large skillet. Add the capers and cook over moderate heat, stirring, until golden and crisp, 1 to 2 minutes. Transfer the capers to a paper towel–lined plate.
Add 2 tablespoons of the oil, half the Brussels sprouts, and half the onion to the skillet. Season with ½ teaspoon salt and ⅛ teaspoon black pepper. Cook over moderate heat, stirring, until crisp-tender, about 5 minutes. Transfer to a large plate. Repeat with the remaining 2 tablespoons of oil, Brussels sprouts, and onion.
Return all the Brussels sprouts to the skillet and stir in the kale, lemon juice, red pepper, and Parmesan. Season with ½ teaspoon salt and stir to combine. Transfer to a serving platter and garnish with the capers and more Parmesan.
Serve warm or at room temperature.
Make-Ahead: Slice the vegetables and refrigerate in airtight containers for up to 2 days.