Preheat oven to 375° and spray a 2-quart baking dish with non-stick spray.
In a skillet over a medium-high heat, add the olive oil, and allow to heat.
Once heated, add the onion, garlic, and carrot. Allow to cook and soften, about 3 minutes.
Add the mushrooms and tomato paste and cook for about 2 minutes.
Reduce the heat to medium-low and stir in the flour, salt, black pepper, paprika, and thyme. Cook for 2 minutes, stirring continuously.
Pour in the vegetable broth and soy sauce.
Add the lentils and peas and allow to cook for about 5 minutes, or until sauce has thickened.
Once thickened, pour into the prepared baking dish and spread into an even layer. Make the mashed potatoes by adding the potatoes to a large stock pot.
Cover the potatoes with cold water. Bring to a boil and cook for about 15 minutes or until very soft and fork tender. Drain the potatoes and put back into the stock pot. Place pot back onto the stove with burner turned off. Let potatoes sit and dry out for about 5-7 minutes.
Microwave almond milk for about 30 seconds. Once potatoes are done resting and drying out, add 1/2 of the warm almond milk, vegan butter, garlic powder, and salt.
Mash potatoes with a potato masher to your desired consistency. If you need to add more milk, do so while mashing, just a splash or two at a time.
Once mashed, spread out an even layer of mashed potatoes over the lentil filling.
Bake for 20-25 minutes, or until potatoes are lightly golden.