In a large pan, heat olive oil. Add onion and broccoli and saute over medium high heat for about 5 minutes.
Add in ground turkey and minced garlic, and cook until turkey is no longer pink.
Add in chili powder, oregano, salt, and pepper. Then add in black beans and green chiles.
Stir in the juice of one lime and 1/4 cup enchilada sauce. Let mixture simmer over medium heat for 2-3 minutes.
In a 9×13 casserole dish, spread 1/4 cup enchilada sauce on the bottom of the dish.
Lay out your flour tortillas and add 1/2 cup mixture to each tortilla. Sprinkle with a little bit of cheese and roll tortillas up tightly. I like to fold the sides in as I am rolling them to create a nice tuck.
Place seam side down in casserole dish. Repeat with remaining tortillas until all mixture is done. Line them up in casserole dish, and place in any empty space remaining.
Top the enchiladas with remaining enchilada sauce and sprinkle with cheese.