There's a well-known Swedish restaurant in Burellton, CA, north of Santa Barbara, that serves a famous pea soup. Here's a reconstruction of their recipe:
PEA SOUP ANDERSEN'S FAMOUS SPLIT PEA SOUP
2 quarts soft water
2 cups split peas
1 branch celery, coarsly chopped
1 large carrot, chopped
1 small onion, chopped
1/4 teaspoon ground thyme
1 pinch cayenne pepper
1 bay leaf
Salt and pepper to taste
Boil all ingredients hard for 20 minutes in a large pot, then reduce heat and simmer until peas are tender.
Strain through fine sieve and reheat to boiling point. Serve.
Actually, I zip it in a food processor and reheat.
Not a complex dish.