Spread out all tortillas on a clean surface at room temperature.
Combine mayonnaise and Dijon mustard in a small bowl until smooth.
Coat each tortilla with a thin layer of the mayo mixture, leaving a small border.
Arrange 2 to 3 slices of turkey over the lower two-thirds of each tortilla, slightly overlapping; then place a slice of cheddar on top.
Evenly layer spinach leaves, shredded carrots, and red pepper strips over the cheese.
Roll each tortilla up tightly from the filled end, folding sides in as you roll.
Wrap each rolled tortilla tightly in plastic wrap and chill in the refrigerator for 30 minutes to set.
Remove wrap and cut each roll-up diagonally in half with a serrated knife; serve or pack for later.