Trim any fat from the chicken thighs and cut into 1/2 - 3/4" chunks
Put the onion, celery, carrot and garlic into a food processor and mince.
Pour the olive oil into a deep heavy skillet and heat over medium high, then add the vegetables and season with 1 teaspoon of the salt. Cook until the vegetables start to dry out a little, stirring often.
Add the chicken, bay leaf and remaining 2 teaspoons of salt. Stir until the chicken starts to brown, about 4 minutes. Raise the heat and add the white wine and cook until the wine has almost evaporated, stirring often.
Stir in the hot broth and then the rice. Bring to a boil, cover, and lower the heat to a simmer. Cook until the rice and chicken chunks are fully cooked, 15-25 minutes depending on your rice and heat. Always taste and make sure the rice is cooked!
Take the pan off the heat and stir in the butter, then the parsley and cheese.
Serve with more grated cheese at the table.