Pick over the split peas, and put them in a soup pot. Tie up the peppercorns and bay leaf in a sachet and add to the peas. Add the veggies, water, and seasonings.
Bring everything to a boil, then reduce to a low simmer. Cover, and cook slowly until the peas have softened, stirring occasionally.
Before serving, remove the spice sachet and the ham hocks. Adjust seasoning to taste.