Heat up 2 tablespoons of the oil in a 12-inch skillet until it's almost smoking. Add the chicken in batches, making sure not to overcrowd it, and brown on both sides. Remove to a plate and set aside.
Add another 1 tablespoon of oil to the skillet and heat until it begins to shimmer, then add the onions, celery, garlic, tomato paste, and thyme cooking over medium heat until the veggies are soft. Whisk in flour and continue to cook for 1 minute. Slowly add sherry and stir, loosening any brown bits on the bottom of the skillet. Add 1 cup of chicken broth and whisk until the mixture is smooth. Carefully pour into the slow cooker.
Add the remaining chicken broth, Better Than Bouillon, black pepper, carrots, and bay leaves to the crockpot. Add the browned chicken, with any accumulated juice, and nestle the pieces in. Cover and cook on low for 4-6 hours, or high for 2-3 hours, or until chicken is tender.
Remove the chicken and transfer to a cutting board. Cool until it can be handled then cut or shred it into bite-size pieces. Remove any fat that's floating on the top of the stew. Remove bay leaves.
Stir in cut chicken, peas, parsley, and heavy whipping cream. Replace cover and turn on High, bringing back to a simmer, while you make the dumplings.