Heat the slow cooker if necessary and heat the oil in a large, heavy-based pan. Add the onions, carrots, and thyme, then gently fry for 15 minutes. Tip the vegetables into the slow cooker pot with the stock. If you're using a chicken carcass, add it now, breaking it in half if you need to. Cover and cook for 2-3 hours on High until the vegetables are tender.
If you used a carcass, remove it now and shred any remaining chicken off the bones. Stir this back into the soup, or add your leftover shredded chicken, if using that instead, plus the peas, and cover and cook for 30 minutes more.
Remove half the mixture, then puree with a stick blender (or ladle half the mixture into a blender or food processor and puree that). Tip back into the pot and check for seasoning.
Mix the yogurt, garlic, and lemon juice, swirl into the soup bowls, then serve with some crusty bread.
