In a saucepan, bring the chicken broth and 2 1/2 cups water to a boil; cover and keep at a simmer.
Meanwhile, in a large saucepan, melt 1 tablespoon butter over medium heat. Add the squash and cook, stirring frequently, until soft, about 5 minutes; transfer to a bowl. Add 2 Tbsp. butter and the onion to the saucepan and cook, stirring, over medium heat until the onion is softened, about 8 minutes. Add the rice and stir until lightly toasted, about 2 minutes. Add the wine and cook, stirring constantly until evaporated, about 2 minutes. Stir in 1/2 cup of the hot broth mixture, bring to a simmer and cook, stirring and adjusting the heat as necessary to maintain a low simmer, until the liquid is absorbed, about 2 minutes. Repeat, adding 1/2 cup of the remaining broth mixture at a time and allowing the liquid to be absorbed, until the rice is tender, about 18 minutes.
Add the cooked squash and the remaining 1 Tbsp. butter. Stir in 1/2 cup parmesan and the parsley; season with salt and pepper. Serve immediately, passing the remaining 1/4 cup parmesan at the table.