In a medium bowl, combine the mayonnaise, minced chipotle peppers, and lime juice to make the chipotle mayo. Mix well and set aside.
In a large bowl, toss the shredded chicken with half of the chipotle mayo until evenly coated.
Spread butter on the outside of each ciabatta roll half. On the inside of the bottom halves, spread the remaining chipotle mayo.
Layer each sandwich with the chipotle chicken mixture, shredded cheese, roasted red pepper slices, red onion, and fresh spinach.
Place the top half of each roll on the sandwiches and press down gently.
Heat a panini press or large skillet over medium heat. Cook the paninis for 4-5 minutes per side, pressing down firmly, until the bread is golden brown and crispy and the cheese is melted.
Remove from heat, let cool for 2 minutes, then slice each panini in half diagonally and serve immediately.