Place the chicken thighs, wild rice, onion, carrots, celery, garlic, white wine, chicken broth, thyme, salt, and pepper into the slow cooker.
Stir gently to combine everything, then cover and cook on low for 6 to 7 hours until the chicken is tender and the rice is cooked through.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir the frozen peas into the mixture.
Mix the heavy cream with the cornstarch in a small bowl until smooth, then pour it into the slow cooker and stir well.
Cover and cook on high for 20 to 30 minutes until the sauce thickens.
While the sauce thickens, bake the biscuits according to the package directions.
Spoon the filling into bowls and top each serving with a warm biscuit.