In a dutch oven over medium heat, fry bacon until crisp. Remove bacon from pot, chop, and set aside. Do not drain grease.
Add onion, carrots, celery, and garlic to the bacon fat and cook until tender, about 5-7 minutes. Add butter and flour and stir for 30 seconds.
Add chicken broth, water, split peas, bay leaves, and thyme. Bring to boil. Cover and reduce heat and continue simmering for about 2 hours, or until split peas are tender and soup becomes thick and creamy.
Remove bay leaves, add chopped bacon, and season to taste with salt and pepper. Garnish with pieces of bread if desired.