Make the filling: In a large, heat-resistant glass bowl, combine the gelatin and broth; stir to mix it together and let it sit for 2 minutes. Heat the gelatin mixture in the microwave on high for 1 ½ minutes, until the gelatin is dissolved (or over medium-low heat in a double boiler for 3 to 4 minutes); set aside.
Heat the oil in a large skillet over medium-high heat. Add the onions and bell peppers; cook until they are softened, 3 to 4 minutes. Add the paprika and annatto; cook for 30 seconds. Add the broth mixture, stirring until the spices are dissolved. Add the potatoes, chicken, peas, parsley, sugar, salt, cumin, oregano, and black pepper; bring the liquid to a boil and cook, uncovered, until the potatoes are tender, about 6 minutes. Adjust seasoning as necessary. Transfer the stew to a medium bowl and set it over a large bowl of iced water to cool it quickly. Cool the stew completely; cover it with plastic wrap and chill it for at least 6 hours or overnight (the mixture will jell).
Make the dough: In a medium saucepan set over medium heat, combine the lard and annatto seeds and heat until they begin to bubble slightly, about 2 minutes. Immediately remove the pot from the heat and steep the seeds for 15 minutes. Strain the lard into a medium bowl; discard the seeds. Cool the lard completely.
In a large bowl, whisk together the flour, sugar, and salt. Make a well in the center and add the egg yolks and cooled lard. Using a wooden spatula, begin to mix everything together while slowly adding enough of the hot water that the dough holds together (it will be wet and sticky) (I used about 2 ½ cups total).
Turn the dough onto a well-floured surface and knead it for 2 to 3 minutes (adding more flour as needed), until the dough is smooth, comes together into a ball, and springs back when gently pressed with a fingertip (if your bowl is large enough, as mine is, I like to just continue the kneading step in the bowl in order to keep my work surface clean). Return it to the bowl; cover the dough tightly with plastic wrap and let it rest for 45 to 60 minutes.
Assemble the salteñas: Line 2 to 3 baking sheets with parchment paper; set them aside. Divide the dough into 26 to 28 equal portions (about 3 ounces / 85 grams each). Roll each piece into a ball, folding the bottom of the dough onto itself so that the ends are at the bottom and the tops are smooth (the way you’d shape rolls). Place them on the prepared baking sheets and cover them with a clean towel; let them rest for 20 minutes.
Working one at a time, flatten each ball slightly into a disc. Line a tortilla press with a zip-top freezer or sandwich bag that has been cut open on three sides so that it opens like a book. Place the disc in the middle of the tortilla press and press the dough into a 6-inch disc about ⅛-inch thick (or roll it out with a rolling pin). Stack the discs with parchment paper in between to avoid sticking.
Place 3 heaping tablespoons of jelled filling in the middle of the disc; bring the edges of the pastry together, letting the dough stretch over the filling. Enclose the filling (press the filling down with your forefinger to compact it). Form a half-moon and, holding it by the top edges, stand it on its bottom, flattening it so it can stand without toppling.
Pinch the edges tightly, and press to form a small rim, about ½ inch wide. Then pinch and fold sections of the rim decoratively to seal it well (as you would a dumpling, by gathering the dough starting at one end and pressing it together at ½-inch intervals, until it’s all sealed). Stand the salteñas on the prepared pans and chill them for at least 20 minutes (or up to 2 hours). Do not crowd the salteñas together on the baking sheet, or their sides will stick and the juices will ooze out.
Bake the salteñas and serve: Preheat the oven to 425°F. Brush the salteñas with the egg wash. Bake them for 35 to 40 minutes, or until they are golden (rotate the pans in the oven halfway through baking, back to front and top to bottom, to ensure that all of the salteñas bake evenly). Transfer the salteñas to a cooling rack. Let them cool for 5 to 10 minutes before serving.