Heat olive oil in a large pan and sauté the onions, carrots, and celery until soft, about 5 minutes.
Add the garlic and mushrooms, and cook until mushrooms release their moisture and shrink, about 7 minutes.
Stir in tomato paste, soy sauce, lentils, and vegetable broth. Simmer for 10 minutes until thickened.
Preheat oven to 375°F (190°C).
Spread the lentil-mushroom mixture into a baking dish, then top with mashed potatoes, smoothing them out.
Bake for 20-25 minutes, or until the top is golden and slightly crispy.
Let cool for 10 minutes before serving.