Makes 6 generous servings
3 tablespoons vegetable oil or half vegetable oil and half butter
1 large yellow onion, diced
3 medium carrots, peeled and diced
2 celery stalks, trimmed and diced
6 cups homemade or reduced-sodium chicken broth, plus additional broth or water, if needed
3 whole smoked turkey wings or 6 smoked turkey wing segments
1 pound green or yellow split peas
Freshly ground black pepper
Heat the oil and butter in a 5-quart heavy pot or Dutch oven over medium heat until the butter is foaming. Stir in the onion, carrots, and celery, season with salt and stir until the vegetables start to sizzle, about 5 minutes. Adjust the heat to low, cover the casserole and cook, stirring occasionally, until the vegetables are tender, about 15 minutes.
Pour in the can of chicken broth, add the turkey wings, and bring to a boil over medium heat. Adjust the heat so the broth is simmering, cover the pot, and cook 30 minutes.
Stir in the split peas and add enough chicken broth or water to cover them completely, if necessary. Bring to a simmer, cover the pot and cook until the split peas are tender and the turkey meat begins to fall from the bone, about 35 minutes. Check the soup occasionally as it cooks; there should be enough liquid to barely submerge the split peas as they cook. If necessary, add more chicken broth or water as the soup cooks. If the turkey wings are done before the split peas, pull them out and let them stand at room temperature until you need them.
When the split peas are tender, remove the turkey wings if you haven’t already done so. At this point you have some options as to how to serve the soup: either leave it as is if you like soup with a chunky texture or, carefully, whisk the soup to break up the peas and give the soup a somewhat smoother texture. Season to taste with salt and pepper. Also, you can serve the turkey wings as is—one section in the bottom of each bowl—or pick the meat from them, discarding the skin and bones, and stir the meat back into the soup. Serving the wings whole is kind of messy, but fun. Shredding the meat is a little more elegant—better for a dinner party or if you plan to freeze a portion of the soup. Serve the soup in warm bowls.