Preheat your oven to 350°F (180°C), or if you’re using a fan oven, set it to 160°C.
In a saucepan, combine the brown lentils with the vegetable stock. Bring the mixture to a boil over medium heat. Once boiling, lower the heat and allow it to simmer. You want to cover the pot with a lid partially.
Season the lentils with ½ teaspoon of kosher salt and let them simmer until they are cooked and soft, which should take about 15 minutes. Once done, remove from heat and set aside. If there's any excess liquid, drain the lentils.
While the lentils are cooking, take another saucepan or a dutch oven and add enough water to cover your potatoes. Bring it to a boil. Once boiling, season with 2 teaspoons of salt and reduce the heat to a simmer.
Cook the potatoes until they’re tender, which should take about 10 minutes.
Drain the potatoes and return them to the pot. Now, mash the potatoes until there are no lumps. Taste the mashed potatoes and season with extra salt if necessary. Add in the vegan butter and almond milk, mixing until just combined and creamy.
In a large skillet, heat the olive oil over medium heat. Once heated, add the mushrooms and sauté for about 3 minutes until they are softened and fragrant.
Next, add the yellow onion, carrot, and celery to the skillet. Sauté until these vegetables are softened, which should take about 3 more minutes.
After the vegetables have softened, add the garlic and sauté for an additional minute.
Sprinkle the sautéed vegetables with 1 tablespoon of all-purpose flour and stir well. Cook for another minute.
Pour in the vegetable stock and stir until well combined. Add the diced tomatoes, soy sauce, smoked paprika, oregano, and black pepper.
Finally, add the cooked lentils and peas, stirring to combine everything.
If your skillet is oven-proof, you can leave the mixture in it. If not, transfer it to a 9×13 inch baking dish. Spread the creamy mashed potatoes evenly over the lentil filling.
Place your skillet or baking dish on a sheet pan to catch any drippings, and bake in the preheated oven for 30 minutes.
Once baked, allow the pie to cool for 5 to 10 minutes before serving.