Peel and clean the carrots and cut into small cubes. Peel and finely dice onion and garlic. Wash basil, shake dry and pluck off the leaves and chop coarsely, up to about 1/4.
Heat the oil. Fry the minced meat for about 5 minutes while turning it until crumbly. Add carrots, onion and garlic and steam briefly. Stir in tomato paste and steam for 4-5 minutes, season with salt and pepper.
Dust with flour and sauté briefly. Add stock and tomatoes. Bring to the boil while stirring, crushing the tomatoes with a spatula. Let the sauce simmer for about 10 minutes while stirring. Season to taste with salt and pepper, stir in chopped basil.
Mix crème fraîche and milk until smooth and season with salt, pepper and nutmeg. Sort the spinach, wash and drain well. Grease an ovenproof dish (approx. 15 x 27 cm). Spread a little crème fraîche thinly on the bottom of the dish.
Place 3 lasagne plates on top. Layer about 1/2 of the minced sauce, 1/3 crème fraîche and about 1/2 spinach. Repeat the process with lasagne sheets, chopped sauce, crème fraîche and spinach. Finish with 3 lasagne sheets and spread the remaining crème fraiche on top.
Grate parmesan and gouda cheese. Spread the cheese on the lasagne. Bake in the preheated oven, 2nd shelf from below (electric oven: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for 45-60 minutes until golden brown. Remove from oven, cut into pieces and garnish with basil leaves.