In a medium saucepan, bring broth to a boil and then reduce to a low simmer. Keep heat on low.
Meanwhile, in another medium saucepan over medium heat, melt 2 tablespoons butter. Add onion and cook, stirring occasionally, until softened, about 5 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute.
Stir rice and bay leaves into onion mixture and season with salt and pepper. Cook, stirring constantly, until rice is coated with the butter and onions and lightly toasted, about 3 minutes.
Use a ladle to add ½ cup of broth, stir, then allow the broth to be almost all absorbed, 2-3 minutes. Keep adding more broth, ½ a cup at a time and allow the broth to get absorbed undisturbed, until all the broth is incorporated, about 20 minutes total.
Remove the saucepan from heat, remove the bay leaves and discard. Stir in the Parmesan cheese and more butter and serve immediately.