Bring a large pot of water to a boil with 1 teaspoon of salt. Add the diced potatoes and cook until they are soft enough to pierce easily with a fork.
Reserve 1 cup of the starchy potato water, then drain the potatoes. Transfer them to a bowl and add the milk, 1/2 cup of the reserved water, 1/2 teaspoon salt, and pepper. Mash until smooth, adding more potato water as needed. Taste and adjust the seasoning.
Dice the onion and mince the garlic. Wash and thinly slice the mushrooms, then peel and finely dice the carrot and celery.
Heat your oven to 375°F (190°C). Use a large oven-safe cast iron pan or have a large, deep baking dish ready.
Heat the olive oil in the pan over medium-high heat. Add the onion and cook for 4–6 minutes, stirring occasionally, until translucent and starting to brown. Add the mushrooms and cook for about 5 minutes, stirring regularly, until soft and reduced.
Reduce the heat to medium. Add the celery, carrot, and garlic. Cook for 3–5 minutes, stirring often, until the vegetables begin to soften.
Remove the pan from the heat. Add the lentils, tomato paste, Dijon mustard, thyme, rosemary, and black pepper. Stir well to coat everything.
Pour in the broth and soy sauce, then stir until everything is well combined. Taste and add more salt if needed.
Spread the frozen peas over the mushroom and lentil mixture. Spoon the mashed potatoes over the top, spreading them evenly and sealing in the filling.
Bake for 40–45 minutes, until the potatoes are lightly browned and the filling is bubbling around the edges. For an extra golden top, broil for 2–3 minutes, watching closely.
Let the shepherd’s pie cool slightly, then garnish with fresh parsley and freshly ground black pepper. Serve warm.