Sweat the onion, celery, carrot and garlic over low heat for 20 minutes, until it caramelises and the flavour deepens. Add paprika for the last few minutes. This can be a bit of a drag if you're just looking to throw everything in the crock pot and go, but is much nicer. By all means, throw and go, though!
Put the sweated veggies into the crock pot with the split peas, the thyme, stock, bay leaf, salt and pepper, and cook on low for 6 hours. You don't want any bite in the split peas at all, they should have simmered into a thick mush (add extra stock or water if too thick). Check for seasoning and don't be afraid to be liberal with the salt if you have used a homemade stock.