Peel and chop the onions and garlic. Peel, wash and dice the carrots. Clean, wash and chop the peppers. Wash and finely chop the chilli. Peel, wash and halve the potatoes and cook in boiling salted water for about 20 minutes.
Heat oil in a pot, add chilli, paprika, carrots, onions and garlic and fry in it. Add the lentils and fry briefly. Add stock and tomatoes, season with salt and pepper and simmer covered over medium heat for 12-15 minutes.
Clean, wash and halve the tomatoes. In the meantime heat milk and butter in a pot. Drain the potatoes, add milk-butter, mash to puree, season to taste with salt, pepper and nutmeg. Add tomatoes to the lentil chili, season to taste and put into an ovenproof dish (approx. 20 x 30 cm).
Spread potato mixture on top. Whisk egg yolk and cream. Brush the surface with the mixture and bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for approx. 12 minutes.