Preheat your oven to 375°F (190°C).
In a mixing bowl, combine flour and sugar. Cut in the vegan butter until the mixture resembles coarse crumbs. Add cold water, one tablespoon at a time, until the dough comes together.
Press the dough into a tart pan. Chill in the fridge for 15 minutes.
In a saucepan, melt the vegan butter for the filling. Add brown sugar and cinnamon, and cook until the sugar dissolves.
Add the apple slices to the saucepan and cook until they are tender and caramelized.
Arrange the caramelized apples over the chilled tart crust.
Bake in the preheated oven for 30-35 minutes, until the crust is golden brown.
Let the tart cool before serving.