In a large 12-inch skillet, heat ghee over medium heat.
Add celery, carrots, potatoes, and onion. Cook for 6–8 minutes, stirring occasionally, until veggies begin to soften.
Stir in thyme, sage, garlic, salt, pepper, and turmeric. Sprinkle arrowroot starch evenly over the vegetables and stir to coat.
Slowly pour in bone broth, stirring constantly to avoid lumps, then add coconut milk.
Nestle the chicken breasts into the mixture. Bring to a boil, then reduce heat to medium-low, cover, and simmer for 10–12 minutes, until the chicken is cooked through and the sauce has thickened slightly.
Remove the chicken to a cutting board and shred into bite-size pieces using two forks.
Return shredded chicken to the skillet, add peas, and stir everything together. Let simmer uncovered for 3–4 minutes to allow the flavors to meld.
Taste and adjust seasoning with more flaky salt or pepper as needed. Sprinkle with chopped parsley or thyme before serving.