Sift the flour into a mixing bowl, then add in small chunks of the chilled vegan butter. Use your fingertips to loosely combine the flour and butter. Lift the flour into the air when doing so, to ensure the mix stays light and airy. Do not overmix or the pastry will become tough. Drizzle in 1-2 tablespoon of water and use a knife to mix it into a dough. Adjust with more water or flour if the dough is too dry or sticky.
Create a dough ball, wrap it in cling film and chill in the fridge for 30 minutes.
Roll the dough on a lightly floured surface to about ¼ inch thickness. In the meantime, preheat your oven to 375°F [190°C (170°C fan)].
Flip the pastry into the tart tin and remove any excess pastry from the edges. Pierce the tart base with a fork, then cover with baking parchment and dried beans or pulses. Blind bake in the oven for 10-12 minutes or until the edges become lightly golden.
Remove from the oven and remove the parchmend and beans/pulses. Allow to cool down completely.
Creating the filling
For the filling, place the vegan feta into a food processor, alongside the lemon juice and basil and process. Add 1-2 tablespoon plant milk to blend it into a smooth mix and season to taste with salt and pepper.
Transfer the whipped feta mix into the cool tart base and refrigerate for a minimum of 30 minutes.
Thinly slice the tomatoes and arrange them on top of the tart. If they are very watery, lightly pat them with a clean kitchen towel before adding them.
For the pesto vinaigrette, blend all ingredients in a food processor and drizzle the pesto mix over the tomato tart.
Garnish with fresh basil leaves and enjoy the tart fresh or store it in the fridge for up to 2 days.