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1. Whisk broth and chipotle together in 2-cup liquid measuring cup. Combine 1/2 cup chipotle broth, rice, and 1/4 teaspoon salt in bowl. Cover bowl and microwave until liquid is completely absorbed, about 5 minutes. Meanwhile, pat chicken dry with paper towels and season with salt and pepper.
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2. Heat 1 tablespoon oil in Dutch oven over medium-high heat until just smoking. Add onion and cook until softened, about 5 minutes. Stir in garlic, chili powder, and cumin and cook until fragrant, about 30 seconds. Add remaining 3/4 cup chipotle broth, parcooked rice, and beans and bring to boil.
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3. Reduce heat to medium-low, add chicken, and cook, covered, until chicken registers 160 degrees and rice is tender, about 15 minutes, flipping chicken half-way through. Transfer chicken to cutting board and rest for 5 to 10 minutes. Cut chicken into 1/2-inch pieces and combine with rice and bean mixture, cheddar, and cilantro in large bowl. Wash now-empty pot.
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4. Whisk flour and water together in bowl. Stack tortillas on plate and microwave, covered, until pliable, about 1 minute. Working 1 at a time, place one-quarter of chicken mixture in center of warm tortilla. Brush edges of tortilla with flour paste. Wrap top and bottom of tortilla tightly over filling. Brush ends of tortilla with paste and fold into center, pressing firmly to seal.
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5. Heat remaining 3 cups oil in clean pot over medium-high heat until 325 degrees. Place 2 chimichangas, seam side down, in oil. Fry, adjusting burner as necessary to maintain oil temperature between 300 and 325 degrees, until chimichangas are deep golden brown, about 2 minutes per side. Drain on wire rack set inside rimmed baking sheet. Bring oil back to 325 degrees and repeat with remaining chimichangas. Serve.
