Place flour in a large bowl. Make a well in the center and add water and salt.
Mix gently with a wooden spoon until the dough comes together.
Cover with plastic wrap and chill for 30 minutes.
In a small bowl, mix the shortening and butter until smooth.
On a lightly floured surface, roll the dough into a rectangle about ¼-inch thick.
Spread half of the shortening mixture over the dough.
Fold one side into the center, spread the remaining shortening on top, then fold the other side over it like a letter.
Roll again into a ¼-inch-thick rectangle and fold into thirds.
Repeat the rolling and folding one more time
Wrap the dough tightly and chill for 8 hours or overnight.
Using a mortar and pestle (or food processor), pound the shallots, parsley, garlic, and chile powder into a paste.
Heat a large skillet over medium heat. Add ground beef and cook until browned, about 5 minutes.
Stir in the shallot paste, diced onion, and beef broth.
Cover and cook, stirring frequently, until the liquid is absorbed, about 10 minutes.
Remove from heat and let cool slightly.
Place a pan of water on the bottom rack of the oven. Preheat oven to 375°F (190°C).
Roll the chilled dough to about ½-inch thick.
Cut into 2½-inch circles.
Spoon about 1⅓ tablespoons of beef filling onto one side of each circle.
Fold over and lightly press the edges to seal.
Arrange patties on a baking sheet and brush tops and edges with beaten egg yolk.
Bake at 375°F for 30 minutes, until puffy.
Reduce oven temperature to 300°F (150°C) and continue baking for 20 minutes, until golden brown.
These patties can also be filled with seasoned chicken or ground turkey.
For parties, they can be made ahead and reheated gently in the oven.
The pan of water in the oven helps create steam, contributing to the puffed texture.
12 servings
1
* The % Daily Value (DV) tells you how much a nutrient in a serving of food contributes to a daily diet. 2,000 calories a day is used for general nutrition advice.