This recipe had near-unanimous raves on epicurious.com, even from avowed former haters of brussels sprouts.
8 tablespoons extra-virgin olive oil, divided
2 pounds brussels sprouts, trimmed, cut in half lengthwise
6 garlic cloves, chopped
1 cup low-salt chicken broth (or water or veggie broth)
1 15-ounce can cannellini (white kidney beans), drained
2 tablespoons (1/4 stick) butter
1 cup (about 4 ounces) coarsely grated young pecorino (softer than an aged cheese)
Heat 3 tablespoons oil in heavy large skillet over high heat. When just about to smoke, add half of brussels sprouts. Cook until brown, stirring occasionally, about 5 minutes. Transfer to large bowl. Heat 3 tablespoons oil in same skillet. Add remaining brussels sprouts, reduce heat to medium-high, and cook until brown, stirring occasionally, about 5 minutes. Transfer brussels sprouts to same bowl. (Alternative — drizzle olive oil over sprouts and roast all at once in oven until nearly tender.)
Add remaining 2 tablespoons oil to skillet; increase heat to high. Add garlic; sauté until brown, stirring constantly, about 1 minute. Add broth and brussels sprouts. Cook until brussels sprouts are crisp-tender, stirring frequently, about 3 minutes. Add beans and butter; stir until butter melts and broth is reduced to glaze, about 1 minute. Season with salt and pepper. Stir in cheese.