How to Make It
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high. Add the poblanos and onion. Cook, stirring occasionally, until tender, about 10 minutes; transfer to a bowl. Wipe the skillet clean. Add the beans to the poblano mixture in the bowl; roughly mash with a fork to combine.
Use 1 tablespoon of the remaining oil to brush 1 side of each tortilla. Place 4 tortillas oiled-side down and top evenly with the poblano mixture and cheese. Cover with the remaining tortillas, oiled-side up.
Heat a skillet over medium-high. Cook the quesadillas in batches, until the tortillas are golden brown and crispy and the cheese is melted, 1 to 2 minutes per side.
Combine the radishes, lime juice, salt, and the remaining 1½ teaspoons of oil in a bowl. Cut the quesadillas into wedges and sprinkle with the dressed radishes, avocado, and cilantro.