Place the potatoes in a large pot and cover with cold water. Add salt to the water. Over high heat, bring the water to a boil, then reduce heat to maintain a low boil. Cook until potatoes are very tender and easily pierced with a fork with no resistance when falling off. About 15-20 minutes.
Drain potatoes well and place back in pot, then return pot to stove. Over low heat, mash potatoes to let the steam escape. Now add butter, 1/4 cup milk, salt & pepper. Mash until smooth & creamy. Add an additional 1/4 cup of milk at a time as needed (*too much milk can make the potatoes soupy). Loosely cover and set aside.
Preheat oven to 400 °F (200 °C). You will need a 9-inch baking dish (or something similar).
Heat a large skillet over medium-high heat. Add oil and wait until it's hot and shimmering. Now add mushrooms and sauté until they have released their moisture, reduced in size and are slightly browned. The pan should be mostly dry (about 7-8 minutes).
Reduce heat to medium and add onions, carrots, and garlic. Sauté until cooked down about 3-4 minutes.
Make a small open space in the pan to add the tomato paste (make sure it's touching the surface of the pan). Cook for 30 seconds and then stir into the veggies.
Add tamari and herbs. Cook for 30-60 seconds until fragrant.
Turn up the heat to medium-high and pour in the red wine. Cook until almost completely reduced, about 2-3 minutes. Turn heat back to medium.
Add the walnuts, broth, and cornstarch/water mixture. Bring to a simmer and cook until thickened, about 3-5 minutes. Stir in thawed peas and cook for 1-2 minutes. Add salt and pepper to taste. Remove from heat.
Using a spatula, place mixture evenly in a casserole dish. Now gently top with mashed potatoes and spread evenly. For texture, you can rake a fork across the top, going both ways. Bake in the oven for 20-30 minutes until heated throughout. For an extra browned top, broil for 1-2 minutes, but watch carefully to prevent burning.
CARROTS: The carrots need to be finely grated to soften and add to the texture of the ground "meat" texture, so don't use matchstick carrots.
WINE: Not all wine is vegan, but there are many varieties out there. Here is a helpful Guide to help you find the right one for you. You can also omit the wine if preferred and replace with 1/4 cup of vegetable broth.