Urban legend has it that the smooshed sandwich came about when a mother put her toddler on the kitchen counter while making a sandwich. The mother turned away for a second and when she looked back her baby had sat on (and thus squashed) the bread.
I love that imagery but it’s more likely this pressed sandwich came about when someone made a no-cook panini by putting a sandwich at the bottom of a picnic basket and letting it get smooshed by the other contents. Whatever the origin, it’s a fun sandwich that kids adore making. There’s something about manipulating and squashing food that gets kids jazzed and this sandwich takes full advantage of that. The fillings are a riff on the BLT, known as the PALT (prosciutto, lettuce, avocado, and tomato) around my house, but feel free to use whatever sandwich fixings your kids like. No matter how you fill it, just make sure you leave yourself adequate smoosh time because a flattened sandwich is all that more fun to eat.