In a large stockpot, heat the olive oil and butter over high heat until hot but not smoking. Add the onion, carrot, and garlic and cook over high heat until softened and slightly browned. Add the scampi shells and cook, turning occasionally, until they are just pink on the outside, about 5 minutes.
Add the cognac and let it evaporate completely. Season the mixture with salt and pepper, then add the tomatoes and boiling water. Bring to a boil and cook at a full boil for 15 minutes.
Meanwhile, in another pot, heat remaining olive oil until smoking. Add remaining onion and carrot and cook until very soft, 15 minutes. Strain the liquid out of the shell pot and pour into second pot with onions and carrots. Bring to a boil and season with salt and pepper. Add peeled scampi and lower heat to a simmer and cook scampi 3 minutes. Ladle into bowls over 1-inch slices of grilled bread and drizzle with good oil.