Preheat the oven to 450°F. Wrap tortillas in foil and place in the oven to warm, setting a timer for 10 minutes and then checking the tortillas' temperature. You want them at-least warm.
Heat ½ tbsp oil in a large skillet or Dutch oven over medium-high. Add the poblanos, remaining chopped onions, cilantro stems, and ½ tsp salt. Cook for about 10 minutes, until everything is tender.
Turn heat down to medium. Add garlic and cook until fragrant, about 1 minute.
Next, add the cooked, drained beans and mix well, warming up the beans again (if they cooled after being drained). Season with pepper. Add cilantro leaves.
Next, assemble the casserole. The layers will be: thin sauce layer; 6 tortillas; half of the beans; one-third of the cheese; 6 tortillas; sauce; remaining beans; one-third of the cheese; 6 tortillas; remaining sauce (spread all the way to the edges); remaining cheese.
Bake until cheese is melted and the sauce is clearly bubbling, about 15 minutes. Allow to cool for 10 minutes.