Make the mashed potatoes first. Boil the peeled and cubed potatoes until soft, about 15-20 minutes. Drain, add the potatoes back to the pot, and add the milk, sour cream, butter, garlic salt, and pepper, to taste. Mash the potatoes with a potato masher or fork until you achieve your desired texture. Add a little bit more milk, if needed, to make them smooth if you don’t like lumps. Set the potatoes aside.
Preheat the oven to 375°F. Heat a large skillet over medium heat and add the oil, mushrooms, onion, and garlic to the skillet. Sauté until the onion turns translucent, about 5-10 minutes, stirring occasionally. Add the lentils, mixed vegetables, soy sauce, tomato paste, vegetable broth, dried parsley, salt, and a pinch of pepper. Stir to combine the mixture. Heat for another 5-7 minutes, stirring occasionally.
Spoon the mixture into a pie dish or an 8x8-inch square baking dish and spread it into an even layer. Carefully dollop and spread 3 cups of the mashed potatoes over top of the vegetable mixture and bake for 20 minutes. (I like to place my pie/baking dish on a baking sheet in case it bubbles over.) Turn the oven to broil and broil for another 5 minutes, until the mashed potatoes start to brown on top. Let cool for about 5-10 minutes before serving.
Note: You will have leftover mashed potatoes to enjoy with another meal during the week or serve to guests separately as a side.