Preheat the oven to 220°C. Line 2 baking trays with baking paper.
Add eggs to a small saucepan, cover with water, and bring to a rolling boil. Boil for 5 minutes, then remove eggs with a slotted spoon and run under cold water. Once cool enough to handle, peel the shells and chop the eggs into chunks. Set aside.
Heat oil in a large frying pan over medium heat. Add mince and cook until brown, about 5 minutes. Remove beef from the pan and set aside. Fry onion, garlic and red capsicum in the pan until the onion has cooked, about 5 minutes.
Add all filling ingredients to a large bowl and toss to combine. Let the filling cool.
Unfold a chilled pastry sheet onto a lightly floured board. Cut out 10cm circles (you can use a saucer to cut around). Add 2 tablespoons of filling into the middle of each circle, wet the pastry edges, then fold over pastry to create a half moon. Use a fork to crimp the pastry edges together. Transfer empanada to a baking tray and brush with beaten egg. Repeat with remaining ingredients.
Bake for 15 minutes, until golden brown and cooked.