Sauté first 3 ingredients in hot oil in a Dutch oven over medium-high heat until tender.
Add rice; cook, stirring constantly, 2 minutes. Reduce heat to medium; add 1 cup broth. Cook, stirring often, until liquid is absorbed.
Repeat procedure with remaining chicken broth, 1 cup at a time. (Cooking time for the rice mixture is about 30 minutes.)
Add wine; cook, stirring gently, until liquid is absorbed. Stir in cheese and butter. Serve immediately.
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