Preheat oven to 350°F (180°C).
Peel and chop shallots. Melt in a pan with butter. Add sliced leeks and chicken broth. Salt and pepper. Simmer at low heat until complete evaporation of chicken broth. Set aside.
Fry chopped meat in a pan with olive oil. Then, add diced tomatoes, tomato sauce, garlic, plucked thyme, and finely chopped basil. Salt and pepper, then cook for about 10 minutes.
In an oiled baking plate 33 cm x 23 cm (13 in. x 9 in.), set three lasagna pastas. Cover with half of the meat sauce and add three more pasta.
Mix cream with leeks mixture and add half of this preparation over pasta. Set another layer of pasta. Cover with the remaining meat sauce and a layer of pasta then finish everything up with leeks mixture. Spread grated cheese.
Oven bake at 350°F (180°C) for 30 minutes. Finish cooking everything up at broil for about 5 minutes.
Cool down for 10 minutes before serving.