Trim the coarse, tough ends from the broccoli rabe and remove any wilted or yellow leaves. Starting at the cut ends of the stems, pull off the tough outer coating of the stems with a paring knife or vegetable peeler. Cut any very thick stems in half lengthwise. Wash the broccoli rabe in plenty of cool water, then drain, leaving some of the water that clings to the leaves.

Heat 2 tablespoons of the oil over medium heat in a large deep, heavy skillet or casserole with a tight-fitting lid. Poke the sausages all over with a fork and lay them in the skillet. Cook, turning as necessary, until caramelized on all sides and no trace of pink remains in the center, about 8 minutes for thinner luganega or up to 12 minutes for thicker sausages. Adjust the heat as the sausages cook so they brown evenly without scorching. Remove the sausages to a plate and cover with aluminum foil to keep them warm. Drain the fat from the skillet without cleaning the pan. Pour in the remaining 2 tablespoons olive oil. Whack the garlic cloves with the flat side of a knife, scatter them over the oil, and cook until golden, about 3 minutes.

Add the broccoli rabe, and season lightly with salt and ¼ teaspoon crushed red pepper. Pour in ½ inch of water, bring to a boil, and cover the casserole. Steam, lifting the lid to stir occasionally, until the broccoli rabe is softened, about 5 minutes. Uncover and cook over medium heat until the liquid is evaporated and the broccoli rabe is tender, about 5 minutes.

Return the sausages to the skillet and turn them until warmed through. Serve the sausages on plates or a platter, flanked by the broccoli rabe.