Rinse the yellow split peas thoroughly under cold water and drain.
In a large pot, heat a bit of oil or butter over medium heat. Add the chopped onion, carrots, celery, and minced garlic. Saut for about 5 minutes until the vegetables start to soften.
If using ham or bacon, add it to the pot and cook for an additional 3-4 minutes until it begins to brown.
Add the rinsed yellow split peas, broth, bay leaf, and dried thyme to the pot. Stir to combine.
Bring the soup to a boil, then reduce the heat to low. Cover the pot and let it simmer for 1.5 to 2 hours, or until the peas are tender and the soup has thickened. Stir occasionally to prevent sticking.
Once the soup has reached the desired consistency, remove the bay leaf and season with salt and pepper to taste.
Use an immersion blender or a potato masher to partially blend the soup, creating a thick and chunky texture. Adjust the thickness by adding more broth if desired.
Serve the Yellow Pea Soup hot, garnished with fresh chopped parsley.
