For the dough: Add the flour and salt to a food processor and pulse to mix. Add the butter and egg. Pulse.
While the processor is running add the water 1 tablespoon at a time until it starts to come together and form a ball.
Turn out onto a floured surface, form into a smooth ball, flatten and wrap with plastic wrap. Refrigerate for 30 minutes.
Chimichurri sauce: Mix all the ingredients except oil in a bowl, then whisk in the oil. Set aside.
Filling: Add vegetable oil to a large sauté pan over medium heat until the oil ripples.
Add the mushrooms and cook, stirring often until the start to brown.
Add the beef, onion, carrot, salt and pepper and cook while breaking up the meat until browned.
Stir in the garlic, cumin and oregano and cook for 2 minutes.
Stir in the tomato puree and simmer for 5 minutes until thickened.
Remove from the heat and stir in the olives. Transfer to a bowl and allow to cool to room temperature. Line a large baking sheet with parchment paper.
Preheat oven to 350F.
Roll the dough to ⅛ inch thick. Cut out 6 inch circles.
Put meat into center of dough circle, brush egg wash around edges and fold in half. Press edge with a fork to seal.
Line them all up on the baking sheet and brush all over with egg wash.
Bake for 25-30 minutes or until golden brown.