In a large Dutch oven, melt the butter over medium low heat. Add the onion, carrot, celery and a little salt and pepper. Cook until the veggies are soft, roughly 8 minutes. Add the garlic and cook for another minute. Stir in the split peas along with the Ham bone, bay leaf, thyme and chicken stock plus the water.
Bring to a boil, then reduce the heat to just a simmer. Leave uncovered for an hour to an hour and half, stirring occasionally, until the split peas are cooked down and the soup is thickened to your desired consistency. If it gets too thick you can just add a little more stock or water. At the very end season with salt and pepper and more thyme if needed. The add the diced ham to heat through just before serving. Add some croutons for a little crunch and a little black pepper.