Bring 3 quarts water to boil with the coarsely chopped onion, carrot, and bay leaf. Prepare the ice bath. Plunge the lobsters into the boiling water and cook for 2 minutes. Remove with tongs and submerge in ice water 1 minute. Drain and set aside.

In a 12 to 14-inch frying pan with 3-inch sides, heat the olive oil and onion and tomato paste over medium heat until softened but not brown, about 8 to 10 minutes. Add the rice and, stirring constantly, cook until opaque, about 2 minutes. Add the white wine, then the lobster cooking liquid, ladle by ladle, until the rice is covered. Turn the heat to high and, stirring constantly, continue to cook, maintaining the level of liquid just above the level of rice, for 10 minutes. Add the mussels and continue cooking 5 minutes.

Remove the lobsters from their shells, chop the meat into 1-inch pieces, and toss into rice, along with the shrimp and soft shell crabs. Continue cooking until rice is soft but still al dente. Season with salt and pepper, remove from heat and stir in butter and parsley. Serve immediately.