Turn the oven to 180 Celsius or 350 Fahrenheit. Meanwhile, add the olives, drained if you've bought them in brine or vinegar, half of the fresh basil leaves, mustard and chilli (you can leave the chilli out if you don't like them) to a container that you can use to mash them altogether. I use the beaker that comes with my hand held blender as I use that to combine them into a smooth paste.
Put the puff pastry on a flat surface like an oven proof baking sheet. Use a pastry cutter or saucer and cut out four circles, each measuring 12cm/5" in diameter.
Turn over the edges of each and pinch them to help them retain their shape. Prick the bases with a fork and using a pastry brush, brush them with some plant-based milk such as almond or brown rice.
Line the tart with baking parchment and fill it with ceramic baking beans or dried pulses. This helps to stop the base becoming soggy and is known as 'baking blind'.
Put the tarts into a hot oven for five to ten minutes.
Remove from the oven and discard the baking parchment and ceramic baking beans or dried pulses.
Divide the olive mixture equally between the four pastry circles. Top with the sliced tomatoes and scatter the pine nuts equally between the four tarts.
Put back into the oven for a further 15-20 minutes and cook until they're brown and the pastry has risen
Just before serving, sprinkle the torn fresh basil over the top of the four tarts and grind some fresh black pepper over them.