Place the beef into a container and cover with water. Soak overnight in the refrigerator to remove excess salt. Drain, rinse, and cut into small cubes before using.

Bring the cubed beef, peas, and water to a boil in a large pot over high heat. Reduce heat to medium-low, cover, and simmer until the peas have softened and mostly dissolved, about 30 minutes. Stir or whisk frequently to help the peas dissolve, and to keep the soup from burning on the bottom of the pot. Stir in the carrots, turnips, and black pepper, continue simmering until the vegetables have softened, about 15 minutes more.