If desired, begin by heating olive oil in a skillet over medium-high heat. Lightly sear the chicken pieces for about 2–3 minutes on each side, just until browned. This enhances flavor but may be omitted for convenience.
Layer the cut chicken, carrots, potatoes, celery, onion, and garlic into the base of the slow cooker.
In a separate bowl, whisk together the chicken broth, tomato paste, thyme, parsley, paprika, salt, black pepper, and flour until no lumps remain.
Carefully pour the seasoned broth mixture over the ingredients in the slow cooker. Stir gently to distribute evenly.
Secure the lid and set to cook—either on low heat for 7 to 8 hours, or on high heat for 4 to 5 hours—until the vegetables are tender and the chicken is thoroughly cooked.
Roughly 15 to 20 minutes prior to serving, mix in the frozen peas. Allow them to heat through during the final phase of cooking.
Spoon the hot stew into individual bowls, top with chopped fresh parsley if desired, and serve alongside crusty bread or warm biscuits.