Arrange peas and carrot in a vegetable steamer over boiling water. Cover and steam 8 minutes or until vegetables are tender. Set aside.
Combine 2 1/2 cups broth and wine in a medium saucepan; place over medium heat. Bring to a simmer; cover, reduce heat, and maintain a very low simmer.
Place remaining 1/2 cup broth in a medium saucepan; bring to a boil over medium-high heat. Add chopped onion and green onions; cook 4 minutes or until tender. Stir in rice. Add 1/2 cup simmering broth mixture to rice mixture; stir constantly until most of the liquid is absorbed. Continue adding broth mixture, 1/2 cup at a time, stirring each time until liquid is absorbed (the entire process should take about 30 minutes). Stir in peas, carrot, cheese, pimiento, and parsley; serve immediately.