Bring the broth to a simmer over medium-high heat. Cover the broth and keep it warm over very low heat.
Melt the butter in a heavy large saucepan over medium heat. Add the onion and saute until translucent, about 8 minutes. Stir in the garlic and saute for 30 seconds. Stir in the rice and cook for about 2 minutes until the rice is toasted. Add the wine and stir until it is absorbed, about 1 minute. Add 3/4 cup of hot broth; simmer over medium-low heat until the liquid is absorbed, stirring often, about 6 minutes. Repeat, adding 3/4 cup of hot broth 2 more times, stirring often, about 12 minutes longer. At this point, the risotto can be made 4 hours ahead. Refrigerate the risotto (the rice will still be firm) and remaining broth, uncovered, until cool, then cover and keep them refrigerated until ready to proceed.
Bring the remaining broth to a simmer, then cover and keep it warm over very low heat. Stir 3/4 cup of hot broth into the partially cooked risotto over medium heat until the broth is absorbed and the risotto is hot, about 3 minutes. Add the remaining broth and simmer until the rice is just tender and the mixture is creamy, about 5 minutes longer. Stir in the peas and parsley. Add the 1/2 cup of Parmesan. Season, to taste, with salt and pepper. Spoon the risotto into bowls. Sprinkle additional cheese over and serve.