Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin tin.
Heat the olive oil in a skillet over medium heat. Add the carrot, onion, and bell pepper. Cook for 5 to 7 minutes, stirring often, until softened. Add the garlic and cook for 30 seconds, then remove the skillet from the heat.
Put the lentils in a large bowl and mash them lightly with a fork, leaving some whole for texture. Stir in the cooked vegetables, rolled oats, egg, tomato paste, soy sauce, thyme, smoked paprika, salt, and pepper until evenly combined.
Divide the lentil mixture among the 8 greased muffin cups. Press it down gently so the portions hold together, then bake for 25 to 30 minutes, until set and browned around the edges.
While the muffins bake, place the potatoes in a saucepan and cover them with water. Bring to a boil, then cook for 15 to 20 minutes, until the potatoes are easily pierced with a fork. Drain well.
Mash the potatoes with the butter, warmed milk, and ¼ teaspoon salt. Keep the texture slightly rustic, adding the milk gradually so the potatoes stay thick enough to sit on the muffins.
Let the muffins rest in the tin for 5 minutes, then lift them out carefully. Spoon the mashed potatoes over each one and serve warm.