Heat 1 tablespoon oil in a large skillet over medium heat. Add onions, carrots, celery, mushrooms, and garlic. Cook until softened and fragrant, about 5 minutes.

Mix in rinsed lentils, tomato paste, soy sauce, thyme, and rosemary. Cook for 1 minute until aromatic, stirring constantly.

Pour in vegetable broth, bring to a gentle simmer. Cook 20–25 minutes, stirring occasionally, until lentils are tender and mixture thickens.

Cut potatoes into even chunks. Cook in salted boiling water for 15–20 minutes until fork-tender. Drain well.

Return potatoes to pot. Add plant-based milk, vegan butter or olive oil, salt, and pepper. Mash until smooth and fluffy.

Spread the lentil filling in a baking dish, top evenly with mashed potatoes. Bake at 375°F for 20 minutes, then broil 2–3 minutes.