Heat 1 Tablespoon of olive oil in a medium frying pan over a medium heat. Cook onions and carrot for 5 minutes until soft. Add garlic and mince and brown (about 5 minutes).
Add all remaining pie filling ingredients, except cornflour and water, stir to combine and simmer for 20 minutes. Stir through the cornflour slurry and cook for a further 2 or 3 minutes until the gravy thickens.
Roll out ⅔ of the pastry to fit a 20-23cm round pie dish. Line the bottom of the dish with the pastry, fill with the mince filling and top with the cheese slices. Roll out the remaining pastry to fit the top of the pie and place on top, sealing the edges with your fingers or a fork.
Prick holes in the pastry using a fork and brush with egg wash. Bake at 180°C/350°F for 40 minutes until the pastry is golden brown and cooked through.
Serve immediately and store leftovers in the fridge for 4 days.
To make mini pies use the same quantities but roll out the pastry and cut rounds that will fit in muffin tins. Pies will only take about 30 minutes to bake.