Rinse the split peas under cold water and remove any debris.
Heat olive oil in a large pot over medium heat.
Add chopped onions and sauté until translucent.
Stir in diced carrots and celery; cook for about 5 minutes.
Add minced garlic and cook for another minute until fragrant.
Pour in the broth and add the rinsed split peas and bay leaf.
Bring the mixture to a boil, then reduce heat to low.
Simmer uncovered for about 45 minutes, stirring occasionally.
Remove the bay leaf and any ham hock before blending the soup for a creamy texture.
Serve hot, garnished with fresh herbs if desired.