Prepare the filling: In a medium bowl, combine the drained flaked tuna, chopped parsley, chopped capers, seasoned mashed potatoes, and ground coriander. Season the mixture with a pinch of salt and black pepper, stirring gently to combine.

Set up the wrapping station: Place one sheet of brik pastry flat on a clean work surface. If using a circular sheet, fold the top and bottom edges slightly inward to create a more manageable shape.

Assemble the filling: Spoon about a quarter of the tuna mixture into the center of the pastry sheet, shaping it into a neat square with a hollow well in the middle.

Add the egg: Carefully crack one whole egg directly into the hollow well of the tuna mixture, making sure the yolk remains fully intact.

Fold the brik: Fold the pastry sheet in half over the filling to form a pocket, sealing the edges firmly so the raw egg does not escape during transfer.

Fry the brik: Heat about 1/2 inch of vegetable oil in a large skillet over medium-high heat. Carefully slide the assembled brik into the hot oil using a wide spatula.

Cook to golden perfection: Fry the brik for about 2 to 3 minutes until the bottom is deeply golden and crispy, then gently flip it over and fry for another 1 to 2 minutes so the egg white cooks while the yolk stays runny.

Drain and serve: Remove the brik using a slotted spoon and let it drain briefly on a paper towel-lined plate. Repeat with the remaining ingredients and serve hot with fresh lemon wedges.