Mix flour with 1 teaspoon salt. Add warm water gradually and knead for 8 to 10 minutes until smooth and supple. Divide into four balls, coat with oil, cover, and rest for 30 minutes.
Prepare the Filling:
Mix beef, onions, remaining salt, black pepper, and paprika gently. Keep the mixture loose rather than compressing it. Combine melted butter and oil in a small bowl.
Stretch and Coil:
Heat the oven to 425 F (220 C). Stretch one dough ball on a lightly oiled surface into a very thin sheet. Trim thick edges, brush lightly with the butter mixture, and scatter one-quarter of the filling along one long edge.
Roll into a loose rope and coil it in the center of the pan. Repeat with remaining dough and filling, continuing the spiral without packing it tightly.
Bake:
Brush with the remaining butter mixture and bake for 35 to 40 minutes until deeply golden. Sprinkle with the finishing water, cover with a clean towel for 10 minutes, then cut into wedges.
Notes
Resting the dough fully makes it easier to stretch without tearing.
Refrigerate baked burek for three days and reheat uncovered in a hot oven.