Melt 2 tablespoons of the butter in a large skillet over medium heat.
Add the onion, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook, stirring occasionally, until softened, 6 to 8 minutes.
Add the rice and cook, stirring, for 2 minutes. Add the wine and simmer until absorbed.
Add half the broth (1 3/4 cups) and simmer, stirring once, until absorbed, 8 to 10 minutes.
Add the remaining broth and simmer, stirring once, until the rice is tender and creamy, 8 to 10 minutes. (If the rice is not cooked through and the mixture is dry, add more broth and continue to cook until tender.)
Stir in the Parmesan and the remaining half tablespoon of butter. Sprinkle with the parsley and additional Parmesan, if desired.