This is the rare Italian sandwich where the fat is named in the title and means it. Most cured-roe panini treat butter as an optional softener; the panino con bottarga e burro makes it a declared half of the structure, a Sardinian pairing that reads almost as a tartine: a thick spread of cold sweet butter on bread, and over it a fall of grated grey-mullet bottarga. The roe is the loud voice, saline and deeply iodine, the egg sac of the mullet salted, pressed, and air-dried to an amber block. But the defining decision here is the butter doing the talking back. Without enough of it the roe is a salt brick; with it the iodine rounds into something nutty and long, and the sandwich becomes about that meeting rather than about the bottarga alone.
The craft is the ratio and the cold. The butter is good and unsalted, spread thick and used cold so it stays a distinct layer rather than melting into the crumb and disappearing; warm butter would slacken into the bread and forfeit the cushion the roe needs to land on. The bottarga is grated fine or shaved to translucence directly over the butter so the two are in contact across the whole surface, never piled in a slab where the salt concentrates and the fat cannot reach it. The bread is plain and fairly neutral, a simple roll or a slice of Sardinian country loaf, present to carry the pairing and nothing else; a flavoured or heavily crusted bread would crowd a balance that is already complete in two ingredients. A few drops of lemon or a thread of olive oil over the top is the entire permitted addition. It is closed and eaten at once, while the butter is firm and the roe freshly cut, because the texture of cold fat against dry roe is the whole sensation and it does not survive sitting.
The variations stay inside the same two-ingredient discipline and each is its own preparation rather than a footnote here: the build on a harder, drier bread so the crust contrasts the unctuous butter, the one finished with lemon alone, the one that swaps butter for a fruity olive oil and becomes a leaner thing. The plain bottarga sandwich without the butter cushion is a sharper, more austere relative that follows its own logic, and it deserves its own article rather than being crowded in here.