Preheat oven to 200⁰C and prepare ingredients as described in list.
Place puff pastry on a tray lined with baking paper (if your pastry comes rolled, you may have to wait until it thaws slightly – best left in the refrigerator for about 30 minutes – before being able to roll out flat). Place another sheet of baking paper over the top, weighed down with baking beans or dried chickpeas, and place in the oven for 20 minutes.
Meanwhile, melt butter and oil together over medium-high heat in a large heavy-based saucepan and add onions and bay leaves. Allow to cook for 5 min, stirring often, before covering for 5 min, lifting the lid and stirring every minute or so to keep onions from burning.
Remove lid and cook for another 5 min. By this point the onions should be more transparent and beginning to brown all over. If there are still some slices of onion that are more opaque and white, continue to cook for a few more minutes.
Add sugar, Herbes de Provence and garlic and stir for a couple of minutes until the sugar is dissolved, the Herbes are fragrant and the garlic is soft. Add the tomato paste, verjuice, tomato, capers and half of the olives. Finely chop half of the parsley and add to the pan, stirring for another 5 minutes.
Remove the baking beans and baking paper covering the pastry and spoon on the onion mixture, leaving a couple of centimetres around the border.
Arrange the anchovies and remaining olives on top. The traditional way is to create a diamond pattern with the anchovy fillets and place an olive piece in the centre of each diamond.
Place back in the oven for 10-15 minutes until the edges of the pastry and crisp and brown.
Toss the remaining parsley, roughly chopped, together with the rocket and a small amount of oil and balsamic, just enough to lightly dress.
Place pissaladière on a wooden chopping board with the rocket salad piled in the centre to serve and chop into rectangular pieces at the table.
If the pastry is done before you have finished steps 3 to 5, then remove from oven and simply set aside. Alternatively you can complete steps 3 to 5, up to a few days in advance and keep the onion mixture refrigerated until ready to cook pastry and assemble.