Tunisian Tuna-and-Egg Turnover

Mash together tuna, scallions, parsley, capers, olive oil, salt, and pepper in a bowl until tuna is broken up and mixture is combined well.
Stir together egg white and water in a cup with a fork.
Put oven racks in upper and lower thirds of oven and preheat oven to 200°F.
Heat 1/2 inch vegetable oil in a 12-inch heavy skillet until it registers 350°F on thermometer.
While vegetable oil is heating, arrange 2 spring-roll wrappers on a work surface and brush centers lightly with olive oil (do not oil edges). Leaving a 1-inch border all around, put 2 tablespoons tuna mixture near lower right corner of 1 wrapper and form mixture into a ring (about 1/2 inch high and 3 inches in diameter) to contain egg.
Repeat procedure with other wrapper. Brush edges of both wrappers with egg white mixture (use separate brushes for oil and for egg white), then break an egg inside each "ring" and season eggs lightly with salt and pepper. Fold top left corner of each wrapper over egg to form a triangle and press edges together to seal.
Immediately lift 1 brik gently by tip of triangle and lower into oil, keeping long side of triangle in center of skillet. Repeat with second brik and fry briks, lapping oil over exposed wrappers with a metal spatula, until undersides are golden, about 1 minute. Flip each brik over sideways with aid of 2 metal spatulas, so long side of each triangle stays in center, then continue to fry, lapping exposed wrapper with oil, until wrapper is golden and egg is cooked but yolk is still runny, about 1 minute more. Transfer to paper towels to drain briefly, then put on a baking sheet and keep warm in oven while making remaining briks.
Make more briks in same manner (using a second baking sheet for keeping last batches warm). Return oil to 350°F between batches.
Serve briks warm.