Make the sauce: In a bowl, whisk the mustard, honey, mayo or yogurt, vinegar, garlic, paprika, salt, and pepper. Taste and adjust sweetness or tang.
Set aside half for dressing the wraps later.
Prep the chicken: Pat the chicken dry. Pound breasts to even thickness for faster, more even cooking. Season lightly with salt and pepper.
Marinate: Toss the chicken with the remaining half of the honey mustard.
Let it sit 20–30 minutes at room temp, or up to 8 hours covered in the fridge.
Preheat the grill or pan: Heat a grill to medium-high, or a grill pan/skillet over medium-high with a light brush of olive oil.
Grill the chicken: Cook 5–7 minutes per side, depending on thickness, until the internal temperature reaches 165°F (74°C) and juices run clear. Let rest 5 minutes, then slice thinly.
Warm the tortillas: Briefly warm each tortilla on the grill or in a dry skillet until pliable (about 15–30 seconds per side). This prevents cracking.
Assemble: Spread a spoonful of reserved honey mustard down the center of each tortilla.
Layer lettuce, tomatoes, cucumber, onion, avocado, and sliced chicken. Add cheese if using.
Wrap it up: Fold the sides inward, then roll tightly from the bottom up. For a sealed edge and a little crunch, place seam-side down on the warm pan for 30–60 seconds.
Serve: Slice in half on a diagonal.
Serve with extra sauce for dipping and a side of fruit, chips, or a simple salad.