Preheat your oven to 375°F (190°C).
In a large skillet, melt the vegan butter over medium heat. Add the chopped onion and garlic, and sauté until they become translucent, about 3-4 minutes.
Stir in the flour to create a roux. Cook for 2-3 minutes, stirring constantly, until the roux begins to turn a light golden color.
Slowly whisk in the vegetable broth and plant-based milk, ensuring there are no lumps. Continue to cook and stir until the mixture thickens, about 5-7 minutes.
Add the diced vegan chicken substitute, carrots, peas, potatoes, dried thyme, salt, and pepper to the skillet. Stir well to combine. Simmer for 10-15 minutes, or until the vegetables are tender and the mixture has thickened to a creamy consistency. Remove from heat.
Roll out one of the pie crusts and place it in the bottom of a pie dish.
Pour the vegan chicken and vegetable filling into the pie crust.
Roll out the second pie crust and place it on top of the filling. Trim any excess dough and crimp the edges to seal the pie.
Cut a few slits in the top crust to allow steam to escape. Brush the top crust with plant-based milk to achieve a golden-brown finish.
Place the pie dish on a baking sheet (to catch any spills) and bake in the preheated oven for 30-35 minutes, or until the crust is golden brown and the filling is bubbling.
Let the Vegan Chicken Pot Pie cool for a few minutes before serving. Slice and enjoy!