In a large bowl, combine flour, sugar, salt, and yeast. Gradually add warm milk and melted butter. Mix until a dough forms.
Knead the dough on a floured surface for about 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place for 1 hour.
While the dough rises, brown the ground beef in a skillet over medium-high heat. Drain off any excess grease. Stir in onion, garlic powder, salt, and pepper. Cook until onion is tender.
Remove from heat and stir in shredded cheese, ketchup, and relish. Set aside.
Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
Punch down the risen dough and divide it into 8 equal portions. Roll each portion into a ball. Flatten each ball into a circle about 6 inches in diameter.
Spoon about 1/4 cup of the meat filling onto one half of each dough circle. Fold the other half of the dough over the filling and pinch the edges to seal, forming a pocket.
Place the pockets on the prepared baking sheet. Brush the tops with the egg wash.