Heat 2 teaspoons olive oil in a large sauté pan over medium heat.
Add the diced red bell pepper and diced white onion. Cook, stirring occasionally, until the onion is translucent and the pepper is softened, about 5–7 minutes.
Add the minced garlic and cook until fragrant, about 30–60 seconds. Remove the pan from heat and transfer the cooked vegetables to a mixing bowl.
Add the sliced black olives, roasted corn, and the cooked shredded chicken to the bowl. Toss to combine.
Mince the chipotle pepper in adobo (or the small fresh jalapeño) and add it to the mixture; toss to distribute. Add fresh minced cilantro to taste, if you like.
Divide the chicken-vegetable mixture into four equal portions. Divide the shredded Monterey Jack cheese into four equal portions.
Wipe the sauté pan clean (or use a clean skillet) and return it to medium heat. Place one flour tortilla in the pan, top with one portion of the filling, then with one portion of the shredded cheese and a little cilantro if desired. Top with a second tortilla.
Cook until the underside is lightly browned and the cheese begins to melt, about 2–4 minutes. Carefully flip the quesadilla and cook the second side until browned and the filling is hot and the cheese is fully melted, about 2–3 minutes more.
Transfer the cooked quesadilla to a cutting board, let rest 1 minute, then cut into quarters. Repeat steps 7–9 with the remaining tortillas, filling, and cheese.