Soften aromatics: In a microwave-safe bowl, combine the onion, garlic, and 1 tablespoon of the butter. Microwave until the onion is slightly translucent, 2–3 minutes, then scrape everything into a 5–6 quart slow cooker.
Whisk the sauce: In the slow cooker, whisk together the cream of celery, cream of chicken, broth, Worcestershire, thyme, poultry seasoning, celery seed, and pepper until smooth.
Add chicken: Nestle the chicken breasts into the sauce, turning to coat. Cover and cook on LOW for 5–7 hours, until the chicken shreds easily with two forks.
Prep dumplings: About 10 minutes before shredding, cut each biscuit into 6 small pieces. Melt the remaining 1 tablespoon butter and toss the biscuit pieces in it to prevent sticking; refrigerate while you finish the stew.
Shred & add veg: Transfer the chicken to a board and shred. Stir the peas and carrots into the slow cooker, return the shredded chicken, and switch the heat to HIGH. Let the mixture bubble, uncovered, for 10–15 minutes to slightly thicken.
Cook dumplings: Scatter the biscuit pieces evenly over the surface. Gently spoon a little gravy over the top. Cover and cook on HIGH for 60–90 minutes, until the dumplings are puffed and set in the center. Quickly lift the lid once around the 45-minute mark to release excess condensation, then cover again promptly.
Finish & serve: Taste and adjust seasoning with additional pepper if needed. Sprinkle with parsley or chives and ladle hot into bowls.