In a medium skillet over medium-high heat, add beef, pork, onion, bell pepper, celery, garlic, oregano, salt, ¼ teaspoon black pepper, red pepper, and paprika. Cook, stirring frequently, until meat is browned and crumbly, about 6 minutes. Drain any excess liquid. Sprinkle with flour and stir to combine. Let cool for at least 10 minutes.
Preheat oven to 400°. Line a baking sheet with parchment paper.
On a lightly floured surface, roll 1 disk of Savory Pie Dough to ⅛-inch thickness. Using a sharp knife or pastry wheel, cut dough into 7 (4×5-inch) rectangles, rerolling if necessary. Place rectangles on prepared pan. Discard scraps. In a small bowl, whisk together egg and 1 tablespoon water. Brush rectangles with egg wash. Spoon about 3 tablespoons meat mixture into center of each rectangle.
On a lightly floured surface, roll remaining disk of Savory Pie Dough to ⅛-inch thickness. Using a sharp knife or pastry wheel, cut dough into 7 (4×5-inch) rectangles, rerolling if necessary. Discard scraps. Place rectangles on top of meat mixture. Using the tines of a fork dipped in flour, crimp edges to seal each pie. Refrigerate until chilled, about 10 minutes. Using a sharp knife, cut 3 slits into top of each pie to vent. Brush top crust with remaining egg wash. Sprinkle with remaining ½ teaspoon black pepper.
Bake until golden brown, 20 to 25 minutes. Let cool slightly on pan; serve warm.
Savory Pie Dough
In a large bowl, whisk together flour and salt. Using a pastry blender, cut in cold butter and shortening until mixture is crumbly.
Slowly pour ½ cup ice water and vinegar into flour mixture. Using a fork, mix until a shaggy dough forms.
Turn out dough onto a lightly floured surface, kneading 3 to 4 times until dough comes together, and shape into 2 disks. Wrap each disk tightly in plastic wrap and refrigerate for at least 1 hour or up to 2 days.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/natchitoches-hand-pies/