In a large dutch oven (5 qt), melt butter over medium-high heat
Add in onion and ½ teaspoon salt. Cook, stirring throughout until onion is softened and fragrant. About 3-4 minutes.
Add garlic, and cook for 30 seconds.
Add water, chicken broth, ham steak, bacon, split peas, thyme, and bay leaves.
Increase heat to high, and bring to a boil, stirring frequently.
Once boiling, reduce heat to low, cover, and let simmer for 45 minutes.
Remove ham steak pieces, and set aside.
Stir in carrots and celery.
Cover, and continue to simmer for 30 minutes.
Meanwhile, use two forks to shred the ham into bite sized pieces.
Once the 30 minutes is up, remove thyme, bacon, and bay leaves and discard.
Add ham in.
Taste, and season with salt and pepper to preference.
Serve.