Prepare one batch of my Perfect Vegan Mashed Potatoes. Cover potatoes with a lid or plastic wrap and set aside until they’re needed.
Preheat your oven to 400°F (approx. 204°C). Grease a 9-x-13- inch (23-x-33-cm) or other shallow 3-quart baking dish with butter. Set aside for now.
Melt the butter in a large skillet or pot over medium-high heat. Add the onion, carrots, and celery and sauté until slightly soft, 3–5 minutes.
Add the corn, peas, garlic, flour, tomato paste, thyme, sage, salt, and pepper and stir until vegetables are evenly coated and the peas and corn are warmed through, about 1 minute.
Stir in the lentils, broth, and wine and bring the mixture to a rapid simmer. Continue cooking, stirring occasionally, until the mixture starts to thicken, about 10 minutes.
Transfer the lentil mixture to your prepared 3-quart dish and smooth over the surface.
Top the lentil mixture with mashed potatoes a little at a time. Note: If your mashed potatoes have dried out a bit, mash in an extra splash or two of non-dairy milk before adding to the casserole dish. Completely smooth over the surface of the potatoes, or leave some peaks and valleys for a more rustic design. If you’re feeling fancy, add a thin layer of mashed potatoes first, then transfer the remaining potatoes to a piping bag with a large star tip and pipe the remaining potatoes over the surface.
Bake for 20 minutes or until the edges start to bubble and brown. Allow the shepherd’s pie to rest 5–10 minutes before serving. Garnish with fresh chopped parsley.