Preheat oven to 400°F.
Melt vegan butter in a skillet over medium-high heat. (I like to cook everything in a large cast iron skillet so that I can transfer it straight to the oven to bake.)
Sauté onions, celery and carrot for 3-5 minutes, until onions are translucent. Add garlic and sauté for 1 more minute.
Sprinkle vegetables with all-purpose flour and stir to coat. Cook for 1-2 minutes, stirring constantly. We simply want to cook out the raw flavor of the flour; we aren't trying to develop any color.
Optionally, deglaze the pan with a splash (about 1/3 cup) dry white wine. Stir and reduce until most of the liquid is gone — this should take just a minute or two.
Pour in vegetable broth and stir to dissolve the flour. Scrape up anything that might be sticking to the bottom of the pan.
Add in the homemade cashew cream (or plant milk) and poultry seasoning (or fresh herbs). Stir to combine.
Fold in the chopped vegan chicken and peas.
Allow the filling to come up to a simmer. Reduce heat to low and allow it to simmer until thickened. (This should only take a minute or two if you are using cashew cream. If you used a store bought plant milk, it may take a few extra minutes, as these tend to have less thickening power. Let it simmer until the filling is thick and creamy.)
This is a good time to taste the filling and add salt and pepper to preference. How much salt is needed will depend on the brand of vegetable broth you're using.
Transfer pot pie filling into a deep dish pie pan or casserole dish. (If you prepared the filling in a cast iron or other ovenproof skillet, you can bake it directly in this.)
Cover with thawed puff pastry sheet and tuck in along the edges of the pan. Cut a few slits in the pastry to allow steam to vent.
Bake for 35-45 minutes, until pastry is puffed up and evenly golden brown and edges are bubbly.