Season the prawns with the salt and pepper. Refrigerate the prawns for 1 hour.
In a large skillet place the olive oil and heat it on medium high until it is hot. Add the chilled prawns and saut, them for 2 minutes on each side, or until they are done. Set them aside and keep them warm.
In a large saucepan place the peanut oil and heat it on medium until it is hot (350°F). Add the leeks and fry them for 1 minute, or until they are golden brown. Remove them with a slotted spoon and place them on paper towels to drain. Lightly season them with the salt.
In each of 4 medium-sized plates with high rims place 1/2 cup of the Prawn-Carrot Sauce. Place 4 prawns on top of the sauce, in a circular pattern. Place the fried leeks on top.
Prawn-Carrot Sauce: In a medium saucepan place the oil and heat it on medium high until it is hot. Add the shells and the heads of the prawns, and saut, them for 4 minutes. Remove them and set them aside.
Add the onions, carrots, and leeks. Saut, them for 5 minutes.
Return the prawn shells and heads to the pan. Saut, the ingredients. Add the white wine. Cook the ingedients for 4 to 6 minutes, or until the liquid is reduced to 1/4. Add the heavy cream. Cook the ingredients on low heat for 12 to 15 minutes, or until the liquid is reduced to 1/2.
Remove the prawn shells and heads with a slotted spoon and discard them. Place the sauce in a food processor and blend it. Strain the sauce and return it to the pan. While whisking constantly, add the pieces of butter one at a time. Season the sauce with the salt and the pepper.