Empty split peas in a colander, and rinse well. Sort through peas to remove any unwanted particles. Set aside. Heat olive oil in large saucepan or stockpot over medium heat. Add carrots and onions. Cook until onions are soft and translucent. Stir in garlic, and cook 30 seconds, stirring constantly so garlic doesn't burn.
Add water or broth, peas, rosemary, bay leaf, and salt. Heat to boiling, and then reduce heat to low. Simmer 30 minutes with lid on and slightly tilted.
Remove peas and vegetables, and discard bay leaf. Transfer peas and vegetables to a food processor or blender. Process until smooth (you may need to do this in two batches, because filling your processor or blender more than half full could cause the hot soup to pop the lid.) Return to saucepan. Cook 5 more minutes, and serve.
Yield: 6 servings (serving size: about 1 cup)