How to Make It
Preheat oven to 400°F. Combine broth, half of the onion, and 4 of the oregano sprigs in a medium saucepan over medium-high; bring to a boil.
Add chicken to pan; reduce heat to medium-low, and keep cooking liquid between 160°F and 180°F. Cook chicken until a thermometer inserted in thickest portion registers 160°F, 25 to 30 minutes. (Keeping the cooking liquid at the right temperature is important. You want it to be steamy, but not bubble at all.)
Remove chicken from cooking liquid, and let cool 15 minutes. Shred chicken. Reserve 2 cups of the cooking liquid.
Finely chop remaining half onion (about 3/4 cup). Combine tomato sauce, chile powder, garlic, flour, cumin, salt, chopped onion, and reserved 2 cups cooking liquid in a medium saucepan over high; bring to a boil. Cook, stirring often, until thickened, 1 to 2 minutes. Reserve 2 cups of the tomato mixture. Add shredded chicken and beans to remaining tomato mixture in pan; toss to coat.
Spoon about 1/3 cup chicken mixture in center of each tortilla, and roll up. Arrange rolled tortillas, seam side down, in a 13- x 9-inch glass or ceramic baking dish coated with cooking spray. Evenly top with reserved 2 cups tomato mixture; sprinkle with cheese. Bake in preheated oven until cheese is melted and sauce is bubbly, about 20 minutes. Top with chopped tomatoes, avocado, and leaves from remaining 2 oregano sprigs (about 2 Tbsp.). Dollop with sour cream.