Add the chicken thighs, sweet potatoes, onion, carrots, celery, chicken broth, flour, thyme, salt, and pepper to the slow cooker. Stir to combine everything evenly.
Cover and cook on low for 6 to 7 hours, until the chicken is cooked through and the sweet potatoes are tender.
Stir in the heavy cream and frozen peas. Let the mixture cook for 10 more minutes while you prepare the brown butter.
Melt the butter in a small skillet over medium heat. Add the sage leaves and cook, swirling the pan, until the butter turns golden brown and smells nutty. Remove from heat.
Pour the sage brown butter into the slow cooker and stir gently to distribute the flavor through the filling.