Preheat the oven to 200C/400F/Gas 6.
For the pastry, place the flour and butter into a food processor and pulse until the mixture resembles breadcrumbs.
Add the egg and pulse again to combine. Add enough water to make the mixture come together into a dough.
Turn the dough out onto a floured surface and lightly knead. Roll the dough out to ½cm/¼in thick and cut out two 18cm/7in circles.
For the filling, heat the oil in a pan and gently fry the onion with the sugar until softened and slightly caramelised.
Sprinkle the onion mixture over the tart bases, along with the grated cheese and the apple slices. Top with the sage leaves.
Place the tarts onto a baking sheet and bake in the oven for ten minutes, or until golden-brown.
To serve, place the warm tarts onto plates.