Mix the flour, salt, and water in a bowl until a sticky dough forms. Knead briefly until smooth, about 2 minutes.
Cover the dough with a damp cloth and let it rest for 10 minutes. This relaxes the gluten and makes rolling easier.
Divide the dough into 4 equal parts. Roll each into a thin rectangle, about 15x20 cm, using a rolling pin.
Place a generous spoonful of cheese near one edge of each rectangle, keeping some space around the filling.
Fold the dough over the filling and pinch the edges tightly to seal. Use a little water if needed to help seal.
Beat the egg and brush the tops of each sealed roll with the egg wash using a pastry brush for a shiny, golden finish.
Heat vegetable oil in a frying pan or deep skillet to 180°C (350°F). Test with a small piece of bread until it bubbles and turns golden.
Carefully place the rolls seam-side down into the hot oil. Fry for about 3-4 minutes per side until golden brown and crispy, flipping gently with tongs or a spatula.
Remove the rolls from the oil and drain on paper towels. Let them rest for 2 minutes to keep the crust crispy.
Serve the crispy fried bread rolls warm, enjoying their crunchy exterior and melted cheese interior with your favorite dips or on their own.