Preheat the oven to 375°F (190°C). Heat a large pot to medium-high heat. Add the olive oil and allow it to heat up. Add the onions and carrots to the pot and sauté them for 3 minutes, until the onions become slightly translucent. Add the garlic and continue to stir for another minute.
Lower the heat to medium and stir in the flour to coat the vegetables. Pour in the plant milk, broth, herbs, and seasoning until the mixture becomes smooth. Stir occasionally as the mixture comes together for 10 minutes.
Remove the bay leaves from the filling and stir in the vegan chicken pieces and peas. Take the filling off of the heat and let it cool for a few minutes. Roll one disk large enough to cover the bottom of the pie pan. Pour the pot pie mixture into the dough-lined pan.
Roll out the second dough to cover the top of the pot pie. Press down on the edges to seal the top and bottom crust really well with the tines of a fork. Poke a few slits into the center of the pie.
Brush the top with plant milk. Bake it for 25-30 minutes or until it's golden brown. Check on it halfway through and cover the edges with a pie crust protector if it looks like they might burn.
Let the pot pie cool down and enjoy! The filling will thicken as it cools.