In a small bowl, combine the first six ingredients (mayonnaise through ground pepper).
Cook chicken and chop into smaller pieces; shred cheese (if needed) and chop one apple. Add these ingredients to a bowl, along with chopped pecans and diced celery.
Add the mayo mixture to the chicken mixture, and mix well to coat.
Portion the chicken salad evenly among bread slices and add spinach, making 4 sandwiches.
Spray both sides of each sandwich with cooking spray, and cook on a panini maker or indoor grill (or just use a sauté pan if you don't have either) until bread is toasted and cheese is melted.
Peel carrots and cut into sticks.
Serve sandwiches with carrots and remaining apples on the side.