1/2 pound large shrimp, shelled and deveined, shells reserved
2 tablespoons vegetable oil
2 tablespoons tomato paste
1 cup dry white wine
6 cups water
1 carrot, halved
1 celery rib, halved
1 small onion, halved
2 tablespoons heavy cream
2 tablespoons snipped chives
Salt and freshly ground pepper
1 package wonton wrappers
4 tablespoons unsalted butter
1 cup cherry tomatoes
1 tablespoon chopped flat-leaf parsley
Freshly grated Pecorino Romano cheese, for serving
Extra-virgin olive oil, for drizzling
Bring a large pot of salted water to a boil. Plunge the lobster into the water head first and cook until it turns bright red, about 7 minutes. Drain the lobster and cool under cold water. Twist off the tail and the claws, then crack them and remove the meat. Chop the meat into 1/2-inch pieces and refrigerate.
Crack the lobster shells and chop the lobster body into 3-inch pieces; transfer to a large saucepan. Add the reserved shrimp shells, vegetable oil and tomato paste and cook over moderate heat, stirring, until sizzling and the shrimp shells turn pink, about 5 minutes. Add the white wine and bring to a boil. Add the water, carrot, celery and onion and bring to a boil. Cook over moderate heat until the broth is reduced to 4 cups, about 1 hour. Strain the broth into a clean saucepan and boil until reduced to 2 cups, about 10 minutes.
Meanwhile, in a food processor, puree the peeled shrimp with the heavy cream. Transfer the puree to a bowl and stir in the lobster meat and chives. Season generously with salt and pepper. Working with 4 wonton wrappers at a time and keeping the rest covered, lightly brush the edges with water. Spoon a level teaspoon of the seafood filling into the center of each wrapper. Fold the wrappers in half over the filling to form triangles and press to seal. Transfer the ravioli to a baking sheet lined with plastic wrap. Cover loosely with a towel and repeat to form the remaining wrappers and filling; you should have about 32.
Melt 1 tablespoon of the butter in a large skillet. Add the tomatoes and cook over high heat, shaking the pan until they begin to burst, about 2 minutes. Add the reduced lobster broth and cook over moderate heat until slightly thickened, about 8 minutes. Swirl in the remaining 3 tablespoons of butter and season with salt and pepper; keep warm over very low heat.
In a large pot of boiling salted water, cook all of the ravioli just until they float, about 1 minute. Drain the ravioli and add to the sauce. Cook over moderate heat, turning, until nicely coated, about 2 minutes. Sprinkle with the parsley and transfer to shallow bowls. Sprinkle with cheese, drizzle with olive oil and serve right away.