Using a dutch oven or heavy bottom pot with tight fitting lid, over medium/high heat, add 1/4 cup olive oil and 2 Tbsp unsalted butter. Once butter is melted and hot, stir in diced onion, grated carrots and 1 tsp salt. Sautee until soft and golden (8-10 min).
Add trimmed, chopped chicken thighs, 2 bay leaves, another 1 tsp salt and 1/4 tsp black pepper. Saute, stirring occasionally until chicken is golden on all sides (5 mins).
Increase the heat to high and add 1 cup white wine. Boil down the wine, scraping the bottom until most of the wine has evaporated.

Add the hot chicken broth, then stir in the rice.
Without separating the cloves (leaving the root end intact), slice the end off a whole head of garlic to expose the garlic cloves. Set the whole head into the center of your rice, sliced side down. Bring to a rolling boil, then reduce heat to low, cover and simmer until rice is fully cooked (15 mins).
Turn off the heat, remove garlic head (you can either push the cloves of garlic out into the rice and eat it or discard it) and quickly stir in remaining 2 Tbsp butter until fully incorporated. Finally, stir in chopped parsley and 1/2 cup parmesan cheese. It should be creamy. Serve right away or leave the lid on to keep it warm until serving. Garnish with more fresh parsley to serve.