Make the dough: Combine flour, salt, sugar, and yeast in a large bowl. Add warm water and olive oil. Mix until a dough forms, then knead for 5–7 minutes until soft and elastic.
Let the dough rise: Place the dough in a lightly oiled bowl, cover, and let it rest in a warm spot for about 1 hour, or until noticeably puffy.
Cook the beef: Heat oil in a skillet over medium heat. Add onion and cook until softened. Add ground beef and break it apart as it cooks.
Season the filling: Once the beef is browned, add garlic, paprika, black pepper, salt, and ketchup. Cook for another 1–2 minutes. If the mixture looks watery, continue cooking until most of the excess moisture is gone.
Add cheese: Remove the skillet from the heat and let the beef mixture cool slightly. Stir in the shredded cheddar cheese.
Divide the dough: Place the dough on a lightly floured surface and divide it into 6–8 equal pieces.
Roll the dough: Roll each piece into a small circle or oval. Keep the dough thick enough that it will not tear when filled.
Fill the pockets: Add a few spoonfuls of the beef and cheese mixture to the center of each piece. Leave space around the edges.
Seal: Fold the dough over the filling and press the edges firmly together. Crimp the edges with a fork to help keep the filling inside.
Prepare for baking: Place the pockets on a parchment-lined baking sheet. Brush the tops with beaten egg. Make a small slit on top of each pocket to let steam escape.
Bake: Bake at 375°F (190°C) for 20–25 minutes, or until the pockets are golden brown and the dough is fully baked.
Rest and serve: Let the Alabama Hot Pockets rest for a few minutes before serving because the filling will be very hot.