If using a store-bought vegan pie crust, you may use it directly from frozen. If homemade, ensure it's well chilled. Prepare the vegan stuffing according to package directions or your recipe; let it cool completely before using.
Cook the vegan chicken pieces until heated through and lightly browned, either by air frying or pan frying. Season lightly if you wish. Set the cooked pieces aside for later use.
Melt the vegan butter in a heavy bottomed pan over medium heat. Add the chopped onion, sliced celery, and sliced carrots, cooking until the vegetables are soft and translucent, about 5 minutes. Stir occasionally to prevent burning. Add the minced garlic, dried thyme leaves, kosher salt, and black pepper. Cook for another minute to let the flavors meld.
Sprinkle the all-purpose flour into the pan, stirring to coat the vegetables well. Cook for 1-2 minutes to eliminate the raw flour taste. Gradually add the vegan vegetable broth, stirring constantly. Once combined and thickened, pour in the vegan heavy cream and toss in the frozen peas. Reduce the heat and simmer for 5-8 minutes, or until the filling is thick. Taste and adjust seasoning if needed. Stir in the cooked vegan chicken pieces from Step 2. Let the filling cool slightly before assembling the pie. I like to taste the filling at this point and add a touch more pepper for a little extra zip.
Preheat your oven to 425°F (220°C) and line a baking sheet with parchment or foil to catch any drips. Spoon the cooled vegetable and vegan chicken filling into the pie crust. Gently press and mound the prepared stuffing on top. Set the pie on the baking sheet and bake for 40-45 minutes. Check after 25 minutes—if the stuffing or crust edges are browning too quickly, loosely cover with foil. Pie is done when gravy bubbles appear at the edge.
Remove the baked pie from the oven and let it cool for about 10 minutes before slicing into wedges and serving. This short rest helps the filling set up for cleaner slices.