Combine water, 1/2 pound baby carrots, celery, tomato, quartered onion, ham bone, 3 cloves garlic, and bay leaves in a large stockpot. Bring stock to a boil. Reduce heat to medium and simmer for 3 hours.
Remove 1 1/2 to 2 cups of the ham meat from the bone, dice, and set aside for use in the soup. Pour stock through a strainer and discard solids. Transfer stock to a covered container and refrigerate until fat rises to the top and solidifies, 1 to 3 hours.
Skim off fat and pour stock into a slow cooker.
Melt butter in a saucepan and add sliced baby carrots, red onion, and 3 cloves diced garlic. Cook and stir until browned, 7 to 8 minutes. Pour wine into the pan and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Add to the slow cooker.
Rinse and drain split peas and add to the slow cooker. Add reserved ham meat, potatoes, sazon seasoning, black pepper, and salt. Stir. Cook on High until soup is thickened, 5 to 6 hours.
Transfer about 1/3 of the soup to a blender. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Return puree to the slow cooker and stir.