Brown the beef and onion in a saucepan. Add the potatoes, peas, stock, paprika, cumin, and salt. Simmer until the beef and potatoes are tender, about 20 minutes.
Sprinkle in the gelatin and stir until dissolved. Transfer to a shallow dish and chill until firm, at least 2 hours.
Make and Fill the Pastry:
Mix the flour, butter, sugar, egg, and salt. Add warm water gradually and knead until smooth. Rest covered for 20 minutes.
Divide into 10 balls and roll into rounds. Place chilled filling in the center, fold, and crimp the edges firmly.
Bake and Serve:
Heat the oven to 425 F. Arrange the salteñas on a lined baking sheet and brush with beaten egg.
Bake until deeply golden, about 25 to 30 minutes. Serve hot with fresh salsa.