In a large mixing bowl, combine the flour, sugar, and salt.

Grate the cold butter directly into the flour mixture. Use your fingers to gently work the butter into the flour until evenly coated.

Add the sourdough discard and cold water. Use your hands to bring the dough together into a shaggy dough. The warmth from your hands will help soften the butter and form the dough into a disc.

If the dough is still very dry, drizzle in a little more cold water as needed. The dough should come together but should not feel wet or sticky.

Shape into a disc, wrap tightly, and chill in the refrigerator for at least 30 minutes.

While the dough chills, melt the butter in a skillet over medium heat.

Add the whisked eggs along with the garlic salt and black pepper. Cook until the eggs are softly scrambled and just set.

Transfer the scrambled eggs to a mixing bowl.

Add the diced ham, smoked gouda, cheddar cheese, and chopped chives. Stir until combined.

Allow the filling to cool slightly before assembling the hand pies.

Roll the chilled dough out on a lightly floured surface to about ⅛-inch thick (3 mm).

Cut 16 squares, approximately 4x4 inches each. Gather and reroll scraps as needed.

Spoon about ⅓ cup filling onto half of the squares.

In a small bowl, whisk 1 egg and brush the edges of the bottom squares with egg wash.

Place another dough square over the top and press around the edges to seal. Use a fork to crimp the borders.

Transfer the hand pies to parchment paper-lined baking sheets. You may need one large baking sheet plus a second smaller one.

Use a knife to cut a small “X” on the top of each hand pie to allow steam to escape.

Chill the assembled hand pies in the freezer for 10 minutes or in the refrigerator for 20 minutes.

Preheat the oven to 375°F (190°C).

Add the milk to the remaining egg wash and whisk together.

Brush the tops of the hand pies generously with egg wash and sprinkle with everything bagel seasoning or poppy seeds if desired.

Bake for 25–30 minutes, rotating the baking sheets halfway through baking for even browning.

For an extra golden crust, broil for 1–2 minutes at the end of baking. Watch carefully — the broiler can go from friend to foe real quick!

Allow to cool slightly before serving.