Season the lamb cubes with salt and pepper. Heat a large skillet over medium-high heat and brown the lamb in batches until all sides are seared. Transfer the browned lamb to the slow cooker.
Add the diced onion, carrots, turnips, tomato paste, and minced garlic to the slow cooker. Pour in the broth and stir to combine everything evenly.
Tuck the thyme and rosemary sprigs into the mixture. Cover and cook on low for 7 to 8 hours until the lamb is fork-tender.
About 15 minutes before serving, stir in the fresh peas. Remove the herb sprigs and taste the broth for seasoning.
Ladle the stew into bowls and sprinkle with chopped parsley before serving.