Boil the potatoes in salted water for 15-18 minutes until fork tender, then drain and steam off excess moisture.
Mash the drained potatoes with vegan butter, plant milk, nutritional yeast, salt, and pepper until smooth and creamy, then set aside.
Saute the onion, carrots, and celery in olive oil over medium heat for 6-8 minutes until softened, then add the garlic and cook for 30 seconds.
Add the chopped mushrooms and cook for 6-7 minutes until they release their liquid and it mostly cooks away.
Stir in tomato paste and cook for 1 minute, then sprinkle with flour and cook for 1 more minute to remove the raw flour taste.
Slowly pour in the vegetable broth while stirring, scraping up browned bits, then stir in tamari and vegan Worcestershire sauce.
Stir in the lentils, thyme, and rosemary, then simmer uncovered for 8-10 minutes until the gravy thickens. Stir in peas during the last 2 minutes, then season with salt and pepper.
Spread the filling evenly in a 9x13 inch baking dish, top with dollops of mashed potatoes, then spread into an even layer and drag a fork across the surface for texture.
Bake at 400°F for 25-30 minutes until bubbling and golden, broiling for the last 2-3 minutes if desired. Let rest for 5-10 minutes before serving.