Make the Dough: Combine flour and salt in a bowl. Cut in cold butter until mixture resembles coarse crumbs. Add ice water gradually until dough forms. Wrap and chill for 15 minutes.
Cook the Eggs: Heat olive oil in a skillet over medium heat. Whisk eggs with black pepper and scramble until just set. Remove from heat and cool slightly.
Preheat Oven: Set oven to 375°F (190°C). Line a baking sheet with parchment paper.
Roll and Cut: Roll dough to 1/8 inch thickness on a floured surface. Cut into 4×6 inch rectangles.
Fill: Place scrambled eggs, ham, and cheese on one half of each rectangle, leaving a border for sealing.
Seal: Fold dough over filling and press edges with a fork to seal completely.
Bake: Place on prepared baking sheet. Brush tops with water or beaten egg. Bake 20-25 minutes until golden brown.