01 - Preheat your grill or grill pan to medium-high heat.
02 - Brush the chicken breasts evenly with olive oil. Season both sides with dried Italian herbs, salt, and black pepper.
03 - Grill the chicken for 6 to 7 minutes per side, or until thoroughly cooked with clear juices. Remove from heat, place on a plate, and allow to rest for 5 minutes before thinly slicing.
04 - While the chicken is cooking, combine the pitted and halved cherries, balsamic vinegar, honey, and Dijon mustard in a small saucepan. Cook over medium heat, stirring occasionally, for 4 to 5 minutes until the cherries soften and the sauce slightly thickens. Remove from heat and let cool.
05 - Briefly warm the flour tortillas in a dry skillet or microwave until they become pliable.
06 - Spread approximately 2 tablespoons of Caesar dressing onto each warm tortilla. Arrange chopped romaine lettuce, sliced grilled chicken, a drizzle of the cherry balsamic sauce, and shaved Parmesan cheese over the dressing.
07 - Sprinkle with freshly cracked black pepper. Tightly roll up each tortilla, folding in the sides to secure the filling. Slice the wraps in half and serve immediately.