1. Heat the oil in a large (13-inch), shallow nonstick braising pan or heavy-duty roasting pan over medium-high heat. Add the onion; cook for 3 to 4 minutes, until just softened.
2. Add the sausage to the pan in small chunks. Cook for 5 to 6 minutes, stirring and breaking up any clumps of sausage, until the sausage loses its raw look; it will not be cooked through. Stir in the tomato and cook for 2 minutes, then stir in the black beans and broth.
3. Add the greens in 1 or 2 batches. Cover (with a lid or aluminum foil) and cook for 2 to 4 minutes to wilt them with each addition; uncover and use tongs to incorporate.
Cover and reduce the heat to medium or medium-low so the liquid is barely bubbling at the edges. Cook for 8 to 10 minutes to meld the flavors and cook the sausage through. Uncover and taste; add salt if desired. If the mixture is soupy, increase the heat to high and cook (uncovered) until the liquid has reduced so the mixture is moist but not soupy. Serve warm or at room temperature.
Makes 8 to 10 side-dish servings or 4 to 6 main-course servings.
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