Preheat oven to 425F. Wash vegetables, peel potatoes and carrots. Dice potatoes, carrots, celery, and onion. Mince garlic. Cut cauliflower into florets. Chop fresh herbs finely.
In a large soup pot, heat 1 tbsp olive oil over medium-high heat. Sear chicken breasts for 4 minutes per side then remove (it will finish cooking fully later).
In the same pot, melt 4 tbsp dairy-free butter over medium heat. Stir in chopped onion and minced garlic, cook for 4-5 minutes until soft.
Add chopped celery, carrot, potato, and cauliflower to the pot and cook for 10-15 minutes while stirring occasionally (vegetables should be partially cooked and softening up). Sprinkle 2 tbsp cornstarch over vegetables and stir to combine.
Stir in the salt, pepper, garlic powder, chopped rosemary, thyme, and sage. Pour in the chicken broth and dairy free milk, bring to a simmer.
Add partially cooked chicken breasts back into the pot and submerge fully under the liquid. Cook while simmering for 15-20 minutes or until the internal temp of the chicken reaches 165F.
Remove fully cooked chicken breasts and transfer to a cutting board. Shred chicken using two forks.
Scoop out about 1/2 of the vegetables (trying to gather as much of the cauliflower as possible) and transfer to a blender. Blend until smooth. Pour creamy mixture back into soup pot and combine. This is what thickens the soup without cream.
Mix in shredded chicken and 1 cup frozen peas. Cook for 5-10 minutes more.
Prepare a large cast iron skillet with one sheet of pastry lining the bottom. Transfer all of the filling inside then cover with the top sheet of pastry. Pinch edges together to seal the pot pie.
In a small bowl, whisk one egg. Brush the egg over the top of the pot pie. Slice two slits for venting in the top. Place in the oven to bake at 425F for 20-25 minutes or until golden brown.