Bring a large pot of salted water to a boil and cook the cavatappi pasta until al dente. Drain and rinse under cold water to stop the cooking and cool the pasta quickly.
In a large mixing bowl, whisk the minced chipotle peppers, lime juice, olive oil, cumin, salt, and black pepper until the dressing is smooth and combined.
Add the cooled pasta, black beans, corn, red bell pepper, red onion, and cilantro to the bowl with the dressing.
Toss gently until every piece is coated with dressing.
Sprinkle the cotija cheese over the top, cover the bowl, and refrigerate for at least one hour before serving.