Start the pastry by whisking the flour, sugar and salt in a large bowl, add the un-melted vegan butter and mix it in until crumbly. Add and mix in the chilled water and oil using a spoon until a dough ball forms.
Cover the dough ball in plastic wrap or foil and chill in the fridge for at least 30 minutes.
When you’re ready to bake your pastry, preheat your oven to 200°C and grease 2 4-inch tart tins with melted butter or oil.
Remove the dough from the fridge, separate into 2 dough balls and roll out onto a lightly floured surface until they’re each about 1/4-inch thick. Gently press each into the tart tins and trim or push in the edges. Use a fork to create holes in the base of the pastry so that air can escape and prevent it from bubbling. Bake in the oven for 25 minutes or until very lightly golden on the edges.
While the pastry is baking, you can start your custard filling by whisking the plant-based milk and arrowroot flour together in a medium-sized pot, then place the pot over low-medium heat. Add all of the other tart ingredients and continue to whisk regularly until it becomes a thick custard consistency. This should take about 10 minutes.
When the crusts are ready, gently pour the custard filling in and place in the freezer for at least 2 hours, but no more than 3 or they will freeze solid. Check that the custard filling is wobbly but still solid enough to bite into.