Ahead of time, pit the cherries.
Position rack in lower third of oven (I also placed a pizza stone on the rack to ensure the base cooked quickly) and preheat to 220°C (425°F).
Whisk sugar, cornstarch, and salt in medium bowl to blend. Stir in cherries, lemon juice, vanilla and almond essence; set aside.
Take the dough disks from the fridge, let them soften a little, then roll out one on floured surface to 12-inch round. Transfer to 9-inch (23cm) glass or ceramic pie dish. Trim the dough around the edge of the dish, then put in the fridge to chill.
Roll out the second dough disc to 12-inch round. Using large knife or pastry wheel with fluted edge, cut strips from dough round (I cut out 14). Lay them on a parchment lined tray or plate and put back in fridge to chill.
Take out the pie dish (lined with dough) from the fridge and spoon the filling and juices into it. Dot with the cubed butter. Brush a little of the milk or beaten egg around the edge of the dough (this will help the lattice strips adhere).
Take the dough strips out of the fridge and arrange over top of the fruit, forming a lattice.*** Where the strips meet the edges of the plate, press gently down to seal. Brush lattice crust with milk or beaten egg and sprinkle with remaining 1 tablespoon sugar. If you have time, put pie into fridge to chill for 15 minutes before baking.
Place pie on rimmed baking sheet and bake 15 minutes. Reduce oven temperature to 190°C (375°F). Bake pie until filling is bubbling (this is important to ensure the cornflour thickens the sauce) and crust is golden brown, covering edges with foil collar if browning too quickly, about 1 hour longer.
Transfer pie to rack and cool completely. It’s important you let the pie sit for 3-4 hours so that the juices thicken and the flavours amalgamate.
Cut into wedges and serve with vanilla ice cream or softly whipped cream.