Preheat the oven to 425°F and arrange an oven rack in the center position. Slice the carrots into ¼-inch half-moons, cut the celery into ¼-inch pieces, dice the onion into ½-inch pieces, and finely mince the garlic. Measure the flour, salt, pepper, thyme, vegetable broth, and vegan heavy cream. Set the pie shell on a baking sheet and reserve it for assembly.

Melt the plant-based butter in a large pot over medium heat. Once the butter is melted and foaming, add the onion, carrots, and celery. Cook for 5–7 minutes, stirring periodically, until the vegetables begin to soften and the onion appears translucent.

Add the minced garlic, kosher salt, black pepper, and thyme. Stir continuously for approximately 1 minute, or until the garlic and seasonings become aromatic.

Scatter the flour evenly over the vegetables. Continue stirring for 1–2 minutes so the flour cooks into the butter and vegetables, forming the roux that will thicken the filling.

Gradually pour in the vegetable broth while stirring continuously to keep the mixture smooth and prevent flour lumps. Once all the broth has been incorporated, allow the sauce to simmer for 2–3 minutes, stirring occasionally, until noticeably thickened and able to coat the back of a spoon.

Stir in the vegan heavy cream, followed by the frozen peas and cooked vegan chicken-style pieces. Simmer everything together for another 5–8 minutes, until the peas are heated through and the sauce develops a thick, creamy consistency. The finished filling should retain body rather than appearing thin or soupy.

Pour the warm filling into the prepared vegan pie shell, stopping approximately ½ inch below the rim to reduce the chance of overflow during baking.

Spread 2–3 cups of unbaked vegan stuffing evenly across the surface of the filling. Break larger portions into bite-size pieces as necessary. Keep the topping relatively loose rather than compressing it so the exposed surface can become crisp while the underside remains moist.

Place the assembled pot pie in the preheated oven and bake for 40–45 minutes, or until the stuffing is golden brown and the filling is gently bubbling around the edges.

Check the topping after approximately 25 minutes of baking. If the stuffing is becoming too dark before the pie has finished cooking, loosely cover the top with aluminum foil and continue baking for the remaining time.

Remove the finished pot pie from the oven and allow it to stand for at least 10 minutes before portioning. This resting period gives the creamy filling time to settle and thicken slightly.