1. Remove the spinach from the freezer. In a medium saucepan, combine the split peas, 3 cups of the water, the unchopped piece of ginger, and 1/2 teaspoon of the salt. Bring to a boil. Reduce the heat and simmer, covered, stirring frequently, until the split peas are tender, about 30 minutes. Add more water if necessary to keep the peas from sticking to the pan.
2. Meanwhile, in a large pot, melt the butter over moderately low heat. Stir in the chopped ginger, the jalapeño, turmeric, coriander, cumin, carrots, potatoes, and the remaining 1 1/4 teaspoons salt. Add the remaining 6 cups water. Bring to a boil. Reduce the heat and simmer, stirring occasionally, until the vegetables are almost tender, about 10 minutes. Stir in the spinach and simmer 5 minutes longer.
3. Remove the whole piece of ginger from the cooked split peas and then stir the split peas into the soup. Simmer the soup for 5 minutes, stirring occasionally.
Wine Recommendation: A simple, straightforward, fruity Beaujolais will make a fine accompaniment to this soup. Its vivid cherry and berry flavors will contrast and highlight, not compete with, the earthiness of the dish.