Cook lentils by adding them and vegetable broth to a medium saucepan and bring to a gentle boil. Lower heat and simmer for 20-25 minutes until lentils are tender but not mushy. Drain excess broth and set aside.

In a large skillet, heat olive oil over medium heat. Add diced onion, carrots, and celery, stirring occasionally for 5-7 minutes until softened. Add minced garlic and sauté for an additional minute.

Stir in the reserved lentils and add tomato paste, dried thyme, paprika, salt, and pepper. Mix thoroughly and cook for another 3-4 minutes.

Peel and cube potatoes, place in a pot of salted water, and bring to boil. Cook for 15-20 minutes until fork-tender. Drain, mash with milk and butter, and season with salt and pepper.

Preheat oven to 400°F (200°C). Spread lentil filling in a baking dish and layer mashed potatoes on top, creating texture with a fork. Bake for 25-30 minutes until golden brown.

Remove from oven, let cool for a few minutes, cut into portions, and serve warm.