In a slow cooker, combine the shredded chicken, diced carrots, celery, peas, and chopped onions. Stir in thyme, garlic, salt, and pepper, blending the flavors together.

In a separate bowl, whisk together the dairy-free milk and gluten-free flour until smooth, ensuring no lumps remain.

Pour the mixture into the slow cooker, gently stirring to incorporate it fully with the chicken and vegetables.

Add the vegetable broth to the slow cooker, stirring gently to combine all the ingredients.

Cover the slow cooker and set it to cook on low for 6-8 hours, or on high for 3-4 hours.

Prepare your gluten-free pie crust according to the package instructions and preheat your oven to 375°F (190°C).

Bake the crust until golden and crispy, about 15-20 minutes.

Once the filling is cooked and the crust is out of the oven, ladle the creamy filling into bowls and top each with a piece of the baked crust.