Peel the prawns, cut them open lengthwise at the back and remove the dark gut. Wash shrimps and shells separately. Dab shrimps dry. Peel onions and garlic and dice finely.
Heat 3 tablespoons of oil in a large pot. Sauté the shrimp shells, peppercorns, half of the garlic and half of the onions in it over a high heat for 4-5 minutes. Season with salt, pepper and about 1/2 teaspoon sugar.
Stir in tomato paste and roast briefly. Deglaze with stock and wine and bring to the boil. Add bay leaf and simmer covered for about 30 minutes.
Cook the pasta in 3-4 l boiling salted water (approx. 1 teaspoon salt per litre) according to the instructions on the packet. Pour the shrimp stock through a fine sieve and collect.
Heat butter in a pot. Fry the rest of the onion cubes until translucent. Dust with flour and sweat lightly. Deglaze with shrimp stock and cream while stirring. Boil up while stirring, add cognac and simmer for about 3 minutes.
Season to taste with salt and pepper.
Heat 1 tablespoon of oil in a frying pan. Fry the prawns for 2-3 minutes, turning them over. Add the rest of the garlic and continue frying for about 1 minute. Season with salt and pepper.
Wash the basil, shake dry and pluck the leaves. Drain the pasta, let it drain and put it back into the pot. Add the sauce, basil and prawns to the noodles and toss everything through.