Prepare the Lentil Base:
Heat olive oil in a large pot or Dutch oven over medium heat. Add onion, carrots, and celery. Cook until softened, about 8-10 minutes.
Add minced garlic and cook for another minute until fragrant.
Stir in rinsed lentils, vegetable broth, diced tomatoes, tomato paste, thyme, rosemary, and smoked paprika. Bring to a boil, then reduce heat, cover, and simmer for 30-40 minutes, or until lentils are tender.
Season with salt and pepper to taste. Stir in frozen peas and corn and cook for 5 minutes more, or until heated through. If the mixture is too liquidy, simmer uncovered for a few extra minutes to thicken.
Prepare the Mashed Potato Topping:
While the lentils are simmering, place peeled and quartered potatoes in a large pot and cover with cold water. Add a pinch of salt. Bring to a boil and cook until fork-tender, about 15-20 minutes.
Drain the potatoes thoroughly. Return them to the hot pot. Add milk, butter, salt, and pepper. Mash until smooth and creamy.
Assemble and Bake:
Preheat your oven to 375°F (190°C).
Pour the lentil mixture into a 9×13 inch baking dish.
Carefully spread the mashed potato topping evenly over the lentil mixture.
Bake for 25-30 minutes, or until the topping is golden brown and the filling is bubbling. If desired, you can broil for the last 2-3 minutes for extra browning.
Let stand for 5-10 minutes before serving.