Preheat: Preheat oven to 400°F with the rack in the middle.
A note: You can prepare the entire recipe directly in an oven-safe skillet, such as cast iron skillet or an enameled braiser. Alternatively, you can prepare the filling on the stove and then transfer it to a deep-dish pie pan or casserole dish.
Sauté the mirepoix: Melt vegan butter in a skillet over medium heat. Sauté diced onions, celery and carrot for 4-6 minutes, or until onions are translucent. Add minced garlic and sauté for 1 more minute.
Form the roux: Sprinkle vegetables with all-purpose flour and stir to coat. The flour will form a paste with the butter (a roux). Cook for 2-3 minutes, stirring constantly, to cook out the raw flavor of the flour.
Deglaze: Deglaze the pan with a splash (about 1/3 cup) dry white wine. (You can substitute vegetable broth or even water in a pinch.) Give it a stir and let it simmer till almost all of the liquid cooks off, just about 1-2 minutes.
Make the sauce: Pour in the vegetable broth and give it a good stir to dissolve the roux. Use your spoon to scrape up any fond from the bottom of the pan. Pour in the prepared cashew cream (or plant milk) and add the poultry seasoning (or fresh herbs). Stir to combine. Then fold in the chopped vegan chicken and frozen peas.
Simmer to thicken: When the sauce starts to bubble, reduce heat to low or medium-low and allow it to simmer till it reaches your preferred consistency. The exact time will vary. Homemade cashew cream should thicken quickly (almost right away). Store-bought plant milk tends to have less thickening power, so it may require a few extra minutes. You can also add an extra splash of water or broth to loosen the consistency. Taste and adjust: Remove the filling from the heat. Taste and season with salt and pepper as needed.