Add olive oil and 2 tablespoons of the unsalted butter to a large pot over medium high heat. Once butter is melted, add onion, carrots, and fresh broccoli (if using). Saute until onions are softened and translucent (about 10 minutes). The mixture should be very fragrant.
Season chicken with sea salt and black pepper then add to pot and saute, stirring occasionally so that it browns on all sides on all sides.
Increase heat to high and add 1 cup white wine. If using frozen broccoli, add in this step. Boil down the wine, scraping the bottom until most of it has evaporated. Add the hot chicken broth, then the rice and stir.
Set the heads of garlic into the center of your rice, cut side down. Bring to a rolling boil, then reduce heat to low, cover and simmer until rice is fully cooked
Turn off the heat, remove garlic heads and stir in remaining 2 tablespoons butter until incorporated. Lastly, stir in parsley and parmesan cheese to make rice creamy.