In a large stock pot over medium high heat, heat the oil. Add the onion and sauté until softened. Add the garlic and stir until fragrant, about 30 seconds. Add the stock, split peas, diced carrot, diced potatoes, soy sauce, basil, black pepper, parsley flakes, ground sage, salt and bay leaves. Stir well to combine. Add the smoked turkey legs (meaty end immersed) and enough water to cover the peas and meaty part of the turkey legs by about an inch. Bring to the boil. Reduce heat and simmer, covered, until the peas have softened (about 45 minutes). Check from time to time to ensure the water level is still above the peas. If not, add a little more water.
Remove the turkey legs and the bay leaves. Discard the bay leaves. When the legs have cooled enough to handle (about 10 minutes), remove the skin and bones from the turkey legs, shredding/chopping the meat into tiny pieces. Set aside.
Using an immersion blender, blend the soup to your desired consistency. (Alternately you can use a food processor or blender.) Add the turkey meat back to the soup and stir to combine. Serve hot.
This soup can be made in a pressure cooker at the high pressure setting, by reducing the cook time to 25 minutes.