Heat the olive oil in a large wide pan. Add the onions, salt and pepper and cook over medium heat. Spread them out evenly in the pan and let cook, stirring occasionally.
As soon as the onions start sticking to the pan, let them stay and brown, but stir them before they burn. The trick is to leave them undisturbed to brown (if you stir them too often, they'll take a lot longer to brown).
Cover and cook for a few mins if they appear too dry and start sticking to the pan. It will take anywhere between 20-30 mins for them to caramelize and soften.
To assemble: butter all the bread on one side. Place half of them on the pan with the buttered side down.
Add a good amount of caramelized onions on top and spread them out evenly. Top with a layer of tomatoes and then mozzarella slices. Add the other slice of bread on top (buttered side up).
Press down the sandwich firmly with a saucepan/mortar. Flip when the bottom side is golden brown. Do the same with the other side. Serve immediately.