Sort through the split peas and remove any foreign matter. Rinse the peas in a strainer, then put them into a bowl with about gallon of water. Soak overnight, or at least four hours.
Combine all the stock ingredients with three quarts of water. Bring to a light boil, then lower to a simmer. Cook for about an hour. Strain the stock into a clean pot, and discard the stock vegetables.
Pour off the soaking water from the peas, and add the peas to the pot of vegetable stock, along with all the other soup ingredients. Bring to a light boil, then reduce to a simmer. Cook for two hours.
Pass the soup through a food mill, or push through a coarse sieve. You can also strain the soup and process the solid parts with a food processor, stopping short of a puree. Add the near-pureed peas to the soup. Adjust seasoning with salt, pepper, and Tabasco to taste.
