Mix together the mayonnaise and pesto in a small bowl. Slice the tomato, then cut those slices in half.
Lay a tortilla flat and spread the mayonnaise mixture over the tortilla. Top with some shredded cheese. In the center of the tortilla, place 2-3 slices of turkey, then follow with the spinach and tomato in the center. Roll the tortilla up over the filling, keeping tight as you roll. Repeat with the other tortilla.
Place the rolls on a plate and refrigerate for about 20 minutes to allow it to firm up. Use a bread knife to cut the rolls into 2” thick slices.
Store in an airtight container for up to a day or enjoy immediately!