Check the beans for any stones or dirt and discard. Put the black-eyed peas in a large bowl; cover with cold water by about 3 inches. Cover, and set aside in a cool spot or the refrigerator to soak overnight.
Drain the black-eyed peas and combine them with the chicken stock and wine in a large saucepan. Bring to a boil and cook, covered, until tender, 45 minutes to an hour.
Meanwhile, heat the oil in a large saute pan over medium heat, tilting the pan to coat. Add the onion and garlic and cook, stirring, until softened, 3 to 4 minutes. Add the sausage and cook until just beginning to brown, 3 to 4 minutes.
When the black-eyed peas are tender, stir in the sausage mixture and reduce the heat to a simmer. Let the black eyed peas simmer until the liquid is completely cooked down and thickened, 2 1/2 to 3 hours.