Flatten bread slices with rolling pin to about 1/8 inch thickness. Trim crusts with serrated knife. Spread 1 side of each slice flattened bread with about 1 teaspoon cream cheese. Top 1 slice with turkey and cheese. Add spinach or lettuce. Top with remaining bread slice, cream cheese-side down. Press sandwich to flatten.
Cut sandwich into 4 quarters with sharp knife. Stack to make 2 sandwiches; press down slightly.
Cut 4 long carrot ribbons with vegetable peeler. Wrap each sandwich with 2 carrot peels, crossing seams underneath sandwich to hold in place.