Rinse 1 cup of split peas under cold water to remove any debris and set aside.
In a large pot or Dutch oven, heat a tablespoon of oil over medium heat.
Add 1 chopped medium onion, 2 chopped medium carrots, and 2 chopped stalks of celery to the pot. Cook, stirring occasionally, until softened, about 5 minutes.
Add 2 minced cloves of garlic to the pot and cook for another minute until fragrant.
Pour in 4 cups of vegetable or chicken broth and bring the mixture to a boil.
Once boiling, add the rinsed split peas to the pot along with 1 bay leaf and 1 teaspoon of dried thyme.
Reduce the heat to low, cover the pot, and let the soup simmer for about 45 minutes to an hour, or until the split peas are tender and the soup has thickened.
Optional: If using, add 1/2 to 1 cup of diced ham or bacon to the soup during the last 15 minutes of cooking for added flavor.
Once the split peas are cooked, remove the bay leaf and season the soup with 1 teaspoon of salt and 1/2 teaspoon of pepper, adjusting to taste.
Serve hot, optionally garnished with chopped fresh herbs or a dollop of sour cream, and enjoy your homemade split pea soup.