RE: Sandwich without bread
Sure. How about an ice cream sandwich? Would a stuffed quesadilla count? Oreo sandwich cookies?
I have this book, SUSAN COSTNER'S GREAT SANDWICHES. In it, there are some unusual choices including a Japanese deep fried eggplant sandwich that has two slices of eggplant on the outside with shrimp and more inside.
There is a Angel food cake sandwich with coffee ice cream and chocolate sauce.
But even this book has very few selections that do not include some type of bread.