In the container of a blender, place arugula, basil, oil, cheese, honey, lemon juice, garlic, salt, and pepper; blend until smooth. Transfer pesto to a large bowl; stir in chicken.
Spoon ¼ cup chicken pesto onto 8 bread slices. Cover with remaining bread slices to make 8 sandwiches. Using a serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches. Cut each sandwich into 3 (3×1-inch) rectangles. Serve immediately, or cover with damp paper towels, place in an airtight container, and refrigerate until serving time.
Recipe by TeaTime Magazine at https://teatimemagazine.com/pesto-chicken-tea-sandwiches/