Prepare the mashed potatoes. Fill a large pot with salted water. Peel and quarter potatoes, and place into pot. Bring to a boil and cook uncovered for 15 minutes, or until a fork inserted into the potato is tender. Drain.

Warm milk in the microwave in 10 second increments, until warm.

Add butter to the potatoes and begin mashing. Pour in milk a little at a time while mashing until you reach desired consistency. Season with salt and pepper. Set aside.

Prepare the lentil filling. Preheat the oven to 400°F.

Combine lentils, thyme and broth in a saucepan and bring to a boil. Reduce heat to a simmer and cover. Cook 20-25 minutes or until the lentils are tender.

Meanwhile, heat olive oil in a skillet over medium high heat. Cook mushrooms, stirring often, until softened, about 8-9 minutes. Reduce heat to medium and add onion, carrots and garlic and cook until tender, another 8-9 minutes. Season to taste with salt and pepper.

Add tomato paste, stir until well combined and cook for 2-3 minutes. Stir in flour and cook for another minute. Add lentils, broth, and peas and cook until thickened. Remove thyme stems.

Transfer lentil filling to a 3-quart casserole dish and spread into an even layer. Top with mashed potatoes.

Bake pie in the preheated oven until potatoes are beginning to brown, about 30 minutes. Let sit at room temperature for 15 minutes before serving.