The day before, place the black olives on an oven tray and leave in the oven all night at 80° to dry them out.
Peel the potatoes, then carve eight 50cm long strips with a vegetable cutter. Soak the strips in cold water. Finely slice the onions with a mandolin and put to one side.
Place the butter in a mixer or mortar and pestle. Then, add the anchovies and garlic. Mix until smooth.
Heat the oven to 170°C.
Drain the potato strips and lay them out on the worktop. Coat them in anchovy butter with the help of a spatula and add a little pepper. Sprinkle a little finely chopped onion on top before rolling up the strips. “Bundle” the 8 potato / onion rolls together and tie delicately with the string. Place on the oven tray, salt lightly and put a few small knobs of butter on top. Place in the oven for around 45 minutes. Every 10 minutes or so, baste the potato pissaladière with the melted butter in the bottom of the tray.
While the potato is cooking, crush the dried black olives and put to one side.
Preheat the oil to 180°C and fry the capers until they are crunchy. Remove and place on kitchen paper to drain the excess oil.
After around 45 minutes, take the potatoes out of the oven and check that they are cooked. Place the potato pissaladière on a serving dish. Replace the string with a piece of raffia. Sprinkle the crushed olives and fried capers on top.