If not already done, cook and crumble your breakfast meat (sausage, bacon, or ham). Set aside.

In a skillet, lightly scramble the 4 large eggs. Cook until just set, then remove from heat and chop into small pieces. If using optional vegetables, sauté them until tender and mix with the cooked eggs.

In a medium bowl, combine the cooked eggs, breakfast meat, shredded cheese, salt, and pepper. Mix well and set aside. Ensure the filling is cool or at least lukewarm before assembling, to prevent the dough from getting soggy.

In a large mixing bowl, whisk together the flour, baking powder, sugar, and salt.

Add the cold cubed butter to the dry ingredients. Using a pastry blender or your fingertips, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.

Pour in the sourdough discard and cold milk. Mix with a fork or your hands until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead gently for 1-2 minutes until it just comes together. Do not overmix.

Form the dough into a disk, wrap it in plastic wrap, and chill in the refrigerator for 15-20 minutes. This makes the dough easier to handle.

Preheat your oven to 400°F (200°C) or your air fryer to 375°F (190°C). Line a baking sheet with parchment paper.

On a lightly floured surface, roll out the chilled dough to about 1/8 to 1/4 inch thick. Use a 4-inch round cookie cutter or a sharp knife to cut out circles or squares. Gather and re-roll scraps as needed.

Place about 2 tablespoons of the breakfast filling on one half of each dough circle/square. Leave a small border around the edge.

Lightly moisten the edges of the dough with water (using your finger). Fold the other half of the dough over the filling to create a half-moon or triangle shape. Press the edges firmly to seal, then crimp with a fork for a decorative finish and extra seal.

Place the assembled pockets on the prepared baking sheet (for oven) or in a single layer in the air fryer basket (for air fryer).

Whisk the remaining large egg for the egg wash. Brush the tops of the pockets with the egg wash for a golden-brown finish.

Oven Method: Bake for 20-25 minutes, or until the pockets are golden brown and cooked through.

Air Fryer Method: Air fry for 12-15 minutes, flipping halfway through, until golden brown and cooked through. (You may need to cook in batches).

Let the breakfast pockets cool for a few minutes before serving. Enjoy warm!