Cut sun-dried tomatoes into thin strips; set aside.
Drain beans in a colander over a medium saucepan; set beans aside. Add wine and broth to reserved canned liquid; bring to a simmer (do not boil). Combine 1/2 cup warm broth mixture and tomatoes in a bowl. Cover; set aside. Keep remaining broth mixture warm over low heat.
Heat oil in a large saucepan over medium heat. Add onion and garlic; sauté 3 minutes. Add rice; cook 1 minute, stirring constantly. Add warm broth mixture, 1 cup at a time, stirring constantly until each portion of broth mixture is absorbed (about 20 minutes total). Add tomato mixture, beans, basil, and salt; cook 2 minutes, stirring constantly. Remove from heat; stir in cheese.