Bring 3 quarts water to boil with the coarsely chopped onion, carrot, and bay leaf. Prepare the ice bath. Plunge each lobster into the boiling water and cook for 2 minutes. Remove and submerge in ice water 1 minute. Drain and set aside. Keep the lobster cooking liquid warm on stove.

In a 12 to 14-inch frying pan with 3-inch sides, heat the olive oil, finely chopped 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 15 minutes.

Remove the lobster from its shell, chop the meat into 1-inch pieces and toss into rice. 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.