Bring 3 quarts water to boil with 1/2 onion, 1/2 carrot and 1 bay leaf. Prepare ice bath. Plunge calamari into boiling water and cook 30 seconds. Remove and submerge in ice water 1 minute. Drain and set aside. Keep cooking liquid warm on stove.
In a 12 to 14-inch frying pan with 3-inch sides, heat olive oil and onion and squid ink over medium heat until softened but not brown, about 8 to 10 minutes. Add rice and, stirring constantly, cook until opaque, about 2 minutes. Add white wine, then shellfish cooking liquid ladle by ladle until rice is covered. Turn heat to high and, stirring constantly, continue to cook, maintaining the level of liquid just above the level of rice, for 15 minutes. Chop the calamari 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.