Whisk broth and chipotle together in 2 cup liquid measuring cup. Combine 1/2 cup chipotle broth, rice and 1/4 tsp salt in microwavable bowl. Cover bowl and microwave until liquid is absorbed, about 5 minutes.
Pat chicken dry with paper towels and season with salt and pepper.
Heat 1 tbsp oil in Dutch oven over medium high heat until just smoking. Add onion and cook for 5 min, stirring occasionally. Stir in garlic, chili powder and cumin and cook for 30 seconds, stirring frequently. Add remaining chipotle broth, parcooked rice and beans and bring to a boil.
Reduce heat to medium low and add the chicken. Cook covered for 10 minutes and then flip the chicken. cover pot again and continue cooking for another 10 minutes.
Transfer chicken to cutting board and let rest for 5-10 minutes. While chicken is resting, remove rice mixture from heat and pour into large bowl. Set aside. Wash now empty pot.
Shred chicken into small pieces and stir into rice mixture along with cheddar and cilantro. Mix well. At this point, you can cool down the chicken and rice mixture and place in refrigerator for up to 2 days before making the chimichangas.
When ready to assemble, whisk flour and water together in a small bowl. Stack tortillas on plate and microwave, covered, until pliable (30 sec-1 min). Working with one tortilla at a time, place one quarter of chicken mixture in center of tortilla. Brush tortilla's circumference with flour and water mixture. The paste will act like a glue, helping you to seal the chimichanga.
Fold opposing sides towards center, one over the other, and press them to seal. Brush top and bottom flaps with paste mixture. Fold flaps in and again press firmly to seal.
Heat remaining 3 cups of oil in the clean Dutch oven over medium high heat to 325 degrees F. Place 2 chimichangas, seam side down, in the hot oil. Fry until chimichangas are deep golden brown, about 2-3 minutes per side. Drain on wire rack set within rimmed baking sheet. Return oil to 325 degrees F. again for remaining 2 chimichangas. Serve.