In a large pot, heat olive oil or butter over medium heat. Add chopped onions and minced garlic. Sauté until onions are translucent.
Add chopped celery, carrots, and diced potato to the pot. Stir to combine with onions and garlic. Cook the vegetables for about 5 minutes until they start to soften.
Pour in the vegetable or chicken broth. Add the bay leaf. Bring the mixture to a boil, then reduce heat to simmer. Cover and cook until the vegetables are tender, about 15-20 minutes.
Add the frozen peas to the pot. Simmer for an additional 5-7 minutes or until the peas are heated through. Remove the bay leaf.
Using an immersion blender or transferring in batches to a regular blender, puree the soup until smooth.
Season the soup with salt and pepper to taste. Serve hot.
