A panino con burrata is defined by a problem the other cheese panini do not have: the filling has almost no structure and wants to leave. Burrata is a Pugliese cheese built as a thin pouch of mozzarella enclosing stracciatella, ragged shreds of fresh curd loosened with cream until the centre is barely held together. Cut it and it does not slice, it spills. Every decision in this sandwich is a response to that. Where a hard cheese is chosen for how it behaves under a knife, burrata is chosen for how mild and how soft it is, and the work is entirely in containing a thing that is closer to a sauce than to a slice and keeping it from turning the bread to paste before the first bite.
The craft is in respecting how little the burrata can take. The cheese is left whole and torn open in the bread, or split at the table, and used at cool room temperature rather than fridge-cold, when the stracciatella reads at its loosest and the cream has not stiffened into something dull. The bread has to do the structural work the cheese cannot: a sturdy crusted roll or a torn piece of a dense loaf, never a soft white slice that would surrender on contact with the cream. The dressing is minimal by necessity, a hard pour of olive oil, coarse salt, a turn of pepper, sometimes a torn basil leaf, because the cheese is mild and any loud addition would simply bury it. Assembly is fast and late: the longer the burrata sits against the crumb the more the bottom gives way, so it is built to be eaten within minutes, not carried.
The variations stay close to the spill problem and the same one-soft-thing logic: the version with stracciatella alone, the bare ragged interior without the pouch; the build with ripe or sun-dried tomato worked against the cream for acid; the burrata set on the dark durum pane di Altamura so a dense Pugliese loaf does the carrying, and the burrata met with prosciutto crudo so a cured meat does the counter-work, which is a distinct gourmet pairing of its own. Each of those is the same collapsing cheese adjusted by one decision, and each deserves its own article rather than being crowded in here.