Place diced potatoes in a large pot, cover with cold salted water, and bring to a boil. Simmer for 15 minutes until tender, then drain and mash with 15 ml olive oil, plant milk, salt, and pepper until creamy. Set aside.

Preheat the oven to 204 °C (200 °C). Heat the remaining 30 ml olive oil in a large oven-safe skillet over medium heat.

Add onion, carrots, and celery to the skillet. Cook for 5 to 7 minutes until vegetables begin to soften. Stir in garlic and mushrooms, cooking for another 5 minutes.

Stir in tomato paste and fresh thyme, cooking for 1 minute until fragrant. Add rinsed lentils, vegetable broth, and soy sauce. Bring to a simmer, cover, and cook for 25 minutes until lentils are tender and liquid is absorbed.

Remove filling from heat and fold in the frozen peas. Taste and adjust seasoning with salt and pepper. Smooth the lentil mixture evenly across the skillet or transfer to a 9x13-inch baking dish.

Spread mashed potatoes evenly over the lentil base, roughing up the top with a fork to create ridges. Bake for 20 minutes until the filling is bubbling and potato peaks turn golden brown. Let sit 10 minutes before serving.