"Haitian patties are different from the Jamaican ones in that they have more of a puff pastry shell, which is less flaky but more puffy. I mostly describe the patties as being like croissants. Great for parties and get-togethers!"
Place flour in a large bowl. Make a well in the center; add water and salt. Mix lightly with a wooden spoon until dough comes together. Cover with plastic wrap and chill for 30 minutes.
Mix shortening and butter together in a small bowl.
Transfer dough to a flat work surface; roll into a rectangle about 1/4-inch thick. Spread 1/2 of the shortening mixture on top. Fold 1 side of the rectangle into the center; spread remaining shortening on top. Fold other side of the rectangle over the first, like a letter. Roll into a 1/4-inch-thick rectangle; fold into thirds. Repeat the rolling and folding process one more time.
Wrap dough with plastic wrap and chill, 8 hours to overnight.
Fill a baking pan with water and place on the bottom rack of the oven. Preheat oven to 375 degrees F (190 degrees C).
Pound shallots, parsley, garlic, and chile powder into paste with a mortar and pestle.
Preheat a large skillet over medium heat; cook and stir beef until browned, about 5 minutes. Stir in shallot paste, onion, and beef broth. Cover and cook, stirring constantly, until juices are absorbed, about 10 minutes. Let cool, about 5 minutes.
Roll chilled dough to a rectangle about 1/2-inch thick. Cut into 2 1/2-inch circles. Place 1 1/3 tablespoon of the beef mixture on 1 side of each circle. Fold and lightly press edges to seal.
Transfer filled patties to a baking sheet. Brush tops and edges with egg yolk.
Bake in the preheated oven until puffy, about 30 minutes. Reduce oven temperature to 300 degrees F (150 degrees C) and continue baking until golden brown, about 20 minutes.