There just aren't enough good recipes around for green split pea soup that don't use a chunk of ham or bacon for flavoring.
Here's a good one that is very simple and very flavorful. Experiment with different combinations of vegetables. If you like hot spices, try adding a chopped jalapeno in with the garlic and ginger.
Cook the split peas with the water and the first group of spices until thoroughly soft, about 45 minutes to an hour.
Heat the olive oil medium-low, and add the ginger and garlic and cook a few minutes. Add the onion and cook until they start to turn transparent. Add the other vegetables and spices, stir and cook 3-5 minutes until they are permeated with the oil. Add the vegetables to the split peas and cook until the potatoes are done, maybe another 15 minutes. Adjust salt and add lemon juice to taste.