Chicken and Rice, Italian style

Easy to make, satisfying one-pot supper adapted from Lidiasitaly.com. 

1-1/2 lbs boneless, skinless chicken thighs
1 medium onion, cut in 1-inch chunks
2 medium carrots, cut in 1-inch chunks
2 ribs celery, cut in 1-inch chunks
2 plump garlic cloves, peeled
1/3 c extra-virgin olive oil
1 T kosher salt, divided
1 bay leaf
1 c dry white wine
5 c hot chicken or turkey stock, plus more if needed
2 c short-grain rice, such as arborio, carnaroli, or paella
2 T butter, cut in pieces
3 T chopped fresh flat-leaf parsley
1/2 c grated Parmesan cheese, plus more for passing

Trim any excess fat from the thighs, and cut into 1-inch chunks. Using a food processor, mince the onion, carrot, celery, and garlic into a fine-textured pestata. Add the oil to a large heavy saucepan, and set over medium-high heat. Stir in the pestata, and season with 1 teaspoon of the salt. Cook for about 5 minutes, stirring frequently, until the pestata has dried and begins to stick to the bottom of the pan. Add the chicken pieces and the bay leaf, and the remaining 2 teaspoons salt. Turn the chicken in the pan until browned all over, about 4 minutes. Raise the heat, pour in the white wine, and cook, stirring and scraping up the browned bits in the pan, until the wine has almost completely evaporated. Add the hot stock with stirring, and then all the rice. Bring to a boil over high heat, cover the pan, and reduce the heat to keep the rice bubbling gently. Cook for about 20 minutes, or until both the rice and the chicken chunks are fully cooked and the consistency is creamy. Off heat, remove the bayleaf, stir in the butter pieces vigorously until thoroughly combined, then stir in the parsley and the grated cheese. Serve immediately in pasta bowls, passing additional grated cheese at the table. Serves 4 to 6.