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 broth, split peas, diced carrot, diced potatoes, soy sauce, basil, black pepper, parsley, ground sage, kosher 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 boil. Reduce heat and simmer, covered, for about 45 minutes, until the peas have softened. Check from time to time to ensure the water level is still above the peas. If not, add a little more water.