Place the onion, carrots, celery, and garlic in a large pot over medium heat. Cook, stirring now and then, until the vegetables soften, about 5 minutes.
Add the split peas, water, bay leaves, and black pepper. Stir to combine.
Bring the mixture to a boil, then lower the heat and simmer uncovered for 45 minutes until the peas are very soft.
Remove the bay leaves. Stir in the thyme and parsley.
Use an immersion blender to puree the soup until smooth, or leave it chunky if you prefer more texture.