Position rack in upper third of oven; preheat broiler to high. Line a baking sheet with foil.
Whisk 1 tablespoon oil and seasoning in a medium bowl. Add cauliflower and poblanos; toss to coat. Spread evenly on the prepared pan. Broil on the upper rack until just tender, about 8 minutes. Reduce oven temperature to 200 degrees .
Top half of each tortilla with 1 tablespoon each beans and cheese and ¼ cup of the vegetable mixture. Sprinkle with the remaining cheese. Fold the tortillas in half.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add 4 quesadillas and cook, flipping once halfway, until browned, 2 to 4 minutes per side. Transfer to the baking sheet and keep warm in the oven. Repeat with the remaining 1 tablespoon oil and 4 quesadillas. Serve the quesadillas with salsa, if desired.
