01 - Preheat oven to 400°F.
02 - Place potatoes in a large pot, cover with salted water, and bring to a boil. Cook until very tender, about 15–20 minutes. Drain and return to pot.
03 - Add milk, butter, sour cream, salt, and pepper to the potatoes. Mash until smooth and creamy. Set aside.
04 - Meanwhile, heat olive oil in a large skillet over medium heat. Add leeks and cook for 3–4 minutes until softened.
05 - Stir in garlic, mushrooms, carrots, and celery. Sauté for 8–10 minutes until mushrooms are browned and vegetables are tender.
06 - Add thyme and flour. Stir and cook for 1 minute.
07 - Pour in vegetable broth, heavy cream, and soy sauce. Simmer for 5 minutes, stirring, until slightly thickened.
08 - Stir in peas, and season the filling with salt and pepper to taste.
09 - Transfer the mushroom and leek mixture to a large baking dish. Spread the mashed potatoes evenly over the top and create ridges with a fork.
10 - Bake for 25–30 minutes, or until the top is golden and the filling is bubbling.
11 - Let rest for 5 minutes before serving.