Combine 3 cups all-purpose flour, 2 teaspoons sugar, and 1 teaspoon fine salt in a large bowl. Add 12 tablespoons cold unsalted butter cut into 1/2-inch cubes. Using a pastry cutter or your fingertips, cut the butter into the flour until mixture resembles coarse crumbs with some pea-sized butter bits remaining.

Add liquid

Whisk the large egg with 6 tablespoons cold water. Drizzle the egg-water mixture into the flour-butter mixture, tossing gently with a fork until it just comes together into a shaggy dough. Do not overwork: you should still see streaks of butter.

Chill and rest

Turn the dough onto a lightly floured surface, gently bring it together into a flat disk (about 1-inch thick). Wrap tightly in plastic and chill in the refrigerator for 30–45 minutes. Chilling firms the butter and makes the pastry flakier.

Frank Filling

Prepare franks

Trim each hot dog or frankfurter into quarters lengthwise or into bite-sized pieces so they are easy to wrap. Pat dry with paper towel.

Sauté onion

Heat 1 tablespoon butter in a medium skillet over medium heat. Add the finely diced onion and sauté until soft and translucent, about 5–7 minutes; do not brown aggressively. Transfer onion to a small bowl and let cool slightly.

Make sauce

In the same skillet over low heat (wipe out if necessary), combine 1 cup ketchup, 2 tablespoons brown sugar, 2 teaspoons Dijon mustard, 1 teaspoon Worcestershire sauce, 1 teaspoon smoked paprika, 1 tablespoon apple cider vinegar, 1 teaspoon salt, and 1 teaspoon black pepper. Stir and warm until the sugar dissolves and flavors meld, about 2–3 minutes. Taste and adjust seasoning.

Combine filling

Return the sautéed onions to the sauce and mix. Add the quartered hot dogs and toss gently to coat. Remove from heat and let the filling cool fully (about 10 minutes). Cooling prevents the pastry from becoming soggy when assembled.

Assembly & Finish

Preheat oven and prepare surface

Position rack in the center of the oven and preheat to 400°F (200°C). Line a baking sheet with parchment paper. Lightly flour your work surface with 1/4 cup flour.

Roll and cut dough

Unwrap chilled dough and place on the floured surface. Roll to a rectangle about 12 x 10 inches and roughly 1/8–1/4 inch thick. Using a sharp knife or pizza cutter, cut the dough into 8 equal rectangles (about 6 x 3.5 inches each).

Portion filling

Spoon about 2–3 tablespoons of the cooled frank filling onto the center of each rectangle, leaving a 1/2-inch border all around. Do not overfill.

Fold and seal

Fold each rectangle in half over the filling to form a packet (or roll like a sausage roll), pressing the edges to seal. Use the tines of a fork to crimp the edges for extra seal and decorative finish. If you prefer a window top, fold one side over and cut a few slits before sealing.

Egg wash and seeds

Whisk the remaining beaten egg with 1 teaspoon water. Brush the tops of each pastry lightly with the egg wash. Sprinkle sesame seeds if using.

Bake

Place the prepared pastries on the baking sheet leaving 1 inch between them. Bake in the preheated 400°F (200°C) oven for 18–22 minutes, until the pastry is puffed and deep golden brown.

Cool and serve

Remove from oven and let cool on the baking sheet for 5 minutes, then transfer to a rack. Serve warm or at room temperature. Optionally serve with extra ketchup or mustard on the side.