Make stock: Combine water, ham bone, baby carrots, celery, tomato, quartered onion, garlic, and bay leaves in a large stockpot. Bring to a boil. Reduce heat to medium and simmer stock for 3 hours.
Remove 1 1/2 to 2 cups ham meat from bone; dice and set aside for use in 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.
Make soup: Melt butter in a large saucepan. Cook and stir baby carrots, red onion, and garlic in hot butter 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 sea salt; stir well.
Cook on High until soup is thickened, 5 to 6 hours.
Transfer about 1/3 of the soup to a blender. Cover and hold the lid down with a potholder; pulse a few times before leaving on to blend. Return purée to the slow cooker and stir.