Warm oil in a large skillet over medium-high heat. Add carrots, onion and celery. Cook, stirring often, until slightly tender, 3 to 5 minutes. Stir in peas and 1 cup water. Bring to a boil, scraping up any cooked bits.
Put ham in a slow cooker and pour pea mixture over it. Cook on low for 4 to 6 hours.
Remove ham and set aside. Season pea mixture with salt and pepper. When ham is cool enough to handle, shred it; discard fat, gristle and bone. Stir meat into peas and spoon over rice. If desired, sprinkle with hot sauce.