In a bowl, mix flour and salt. Cut in cold butter using a pastry blender until mixture resembles coarse crumbs with pea-sized butter chunks.

Add cold sourdough discard and mix gently until a shaggy dough forms. Knead briefly on a floured surface to bring together.

Wrap dough in plastic wrap and chill for at least 30 minutes.

Whisk 4 eggs with milk, salt, and pepper. Scramble in a skillet until soft curds form (slightly undercooked). Remove from heat and cool completely.

Stir diced ham and cheese into the cooled eggs.

Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.

Roll dough out to 1/8 inch thickness. Cut into 6-8 rectangles.

Place filling on one half of each rectangle. Fold over and crimp edges with a fork to seal.

Cut steam vents in tops and brush with beaten egg wash.

Bake for 20-25 minutes until puffed and golden brown.