Brush the outside of the naan with the butter and place two halves on a hot grill. Layer with Daiya shreds, Daiya swiss slices, sliced tomatoes, arugula and more of the swiss slices. Place the other naan on top and allow to cook until golden brown. Flip and cook until golden brown and the cheese is melty. This should be about 10 minutes.
Slice the grilled cheese into wedges and drizzle with maple syrup to serve.