Heat oil in a large nonstick skillet over medium-high heat. Add shallots, bell pepper, oregano, and garlic to pan; cook 12 minutes or until the vegetables are tender, stirring frequently. Remove from heat. Stir in broth, vinegar, and 1/4 teaspoon salt. Cover and set aside.
Bring 3 cups water and chile to a boil in a medium saucepan; add rice. Cover, reduce heat, and simmer 18 minutes or until liquid is absorbed. Remove from heat; fluff with a fork. Stir in remaining 1/4 teaspoon salt and beans. Spoon 1 cup rice mixture onto each of 6 serving plates; top each serving with about 1/4 cup shallot mixture.
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