In a large bowl, whisk together the flour, salt, and sugar. Add the cold butter cubes and cut them into the flour with a pastry cutter or your fingertips until the butter pieces are about pea-sized and still visible.

In a small bowl, whisk together the ice water, 1 egg, and vinegar. Drizzle this mixture over the flour-butter mixture, tossing gently with a fork until the dough just comes together. Add an extra tablespoon or two of ice water only if there are dry patches.

Turn the dough out onto a lightly floured surface and gently press it into a rough rectangle without overworking. Divide into 2 equal pieces, shape each into a flat rectangle, wrap tightly in plastic, and chill for at least 1 hour.

While the dough chills, make the filling. Cook the chopped bacon in a skillet over medium heat until crisp. Transfer to a paper towel–lined plate to drain and cool. Discard all but 1 teaspoon of the bacon fat.

In a bowl, whisk together the 4 eggs, milk, smoked paprika, salt, and black pepper. Add the butter to the skillet with the reserved bacon fat over low heat, then pour in the egg mixture. Cook, stirring gently, until the eggs are just softly scrambled and still slightly glossy. Remove from heat and let cool completely.

Stir the cooled scrambled eggs with the cooked bacon, shredded cheddar, and green onion or chives. Taste and adjust seasoning if needed, keeping in mind that the pastry is mild. Let the filling cool to room temperature and blot with a paper towel if it seems wet.

Line 2 baking sheets with parchment paper. On a lightly floured, cool surface, roll out one piece of chilled dough into a rectangle about 1/8 inch thick. Trim the edges to square them off, then cut into 8 equal rectangles, about 3 x 4 inches each. Repeat with the second piece of dough to make 16 rectangles total. Chill the cut rectangles in the fridge for 5–10 minutes if they soften.

Place 8 rectangles on one prepared baking sheet, spacing them slightly apart. Spoon 2–3 tablespoons of filling onto each rectangle, spreading it into an even layer and leaving a clean 1/2-inch border on all sides. Do not overfill.

In a small bowl, whisk together the egg and milk for the egg wash. Lightly brush the exposed borders of each filled rectangle with egg wash.

Top each filled rectangle with a second rectangle of dough, pressing gently around the edges to seal. Use a fork to crimp all the way around each pop-tart to lock in the filling.

Use a sharp knife or skewer to poke 3–4 small steam vents in the top of each pastry. Brush the tops lightly with more egg wash. Transfer the tray to the refrigerator or freezer for 10–15 minutes so the dough firms up.

While the pastries chill, preheat the oven to 400°F (200°C).

Bake the pop-tarts for 20–25 minutes, rotating the pan halfway through, until the pastry is puffed and deep golden brown at the edges.

Let the pop-tarts cool on the baking sheet for 5–10 minutes before serving so the filling sets slightly. Serve warm, or cool completely for storing and reheating later.