In a blender or food processor, puree the chipotles in adobo. Reserve 3 tbsp. for this recipe. Place the rest in a resealable freezer bag, press to the bottom of the bag, roll up, label and freeze for the next time you need chipotle paste.
Prepare a large bowl of ice water. In a large skillet, bring a few inches of water to a boil. Salt the water, add the broccolini and cook until crisp-tender, about 3 minutes. Transfer to the ice water. Drain; thinly slice on an angle.
In a large skillet, heat the oil, two turns of the pan, over high. Add the broccolini, pepper and onion; stir-fry until the pepper and onion are crisp-tender, 3 to 4 minutes. Add 3 tbsp. chipotle paste, the garlic, tomato and cilantro. Toss until the tomato softens, 1 to 2 minutes more; season with salt and pepper.
Spray a large nonstick skillet with cooking spray; heat over medium-high, Add 1 tortilla to the skillet and cook until browned in spots, about 1 minute. Turn over, top half the tortilla with some of the cheese (about 1/2 cup), a quarter of the veggies and more cheese (about 1/4 cup). Fold the tortilla in half and cook until the tortilla is crispy and the cheese melts, turning once, 1 to 2 minutes. Repeat with the remaining tortillas, cheese and vegetables.
Cut each quesadilla into 4 wedges.