Crumble the feta into a medium bowl. Add the softened cream cheese, egg yolk, dried oregano, black pepper and chopped parsley (if using). Mix thoroughly with a fork until the mixture is smooth but still has some texture. Taste and adjust seasoning if desired. Transfer the filling to a piping bag or a bowl and cover; chill for 15–20 minutes to firm slightly.

Wrapping

Lay out one sheet of fillo on a clean work surface and lightly dust with flour and/or sprinkle a little cornstarch if using to reduce sticking. Brush the entire sheet lightly with melted butter. Place a second fillo sheet on top and brush again. Cut the double-layered stack crosswise into 3 or 4 equal strips, about 6–8 cm (2½–3 in) wide depending on desired roll size.

Place roughly 1 to 1½ tablespoons of the chilled cheese filling near one short end of a strip (leave a 1 cm/½ inch margin at the edge). Fold the bottom edge over the filling, then fold the sides in once to enclose, and continue rolling tightly to form a neat cylinder. Brush the final edge with a little melted butter to seal. Repeat with remaining strips and filling. You should get about 12–16 rolls depending on strip width.

Breading & Frying

Prepare breading station

Set up three shallow dishes: (1) flour, seasoned with a pinch of salt; (2) beaten eggs mixed with 2 tablespoons cold water to make an egg wash; (3) breadcrumbs seasoned with 1 tsp salt. Place the wrapped rolls on a tray.

Coat the rolls

Working in batches, lightly dredge each roll in flour, shaking off excess. Dip into the egg wash, then roll in breadcrumbs, pressing gently to adhere an even coating. Place coated rolls on a tray and refrigerate for 10 minutes to help the coating set (this reduces breading separation during frying).

Heat oil

Pour vegetable oil into a deep heavy pot or deep fryer to a depth of about 6–8 cm (3 inches). Heat to 175°C (350°F). If you don't have a thermometer, test by dropping a small breadcrumb into the oil — it should sizzle and become golden in about 30–40 seconds.

Fry the rolls in small batches (do not overcrowd) for 2½–4 minutes, turning occasionally with a slotted spoon or spider, until evenly golden brown and crisp. Keep oil temperature steady — adjust heat as necessary. Use a thermometer or watch color carefully so cheese does not burst through the coating.

Remove fried rolls to a paper towel–lined tray to drain. Sprinkle lightly with a pinch of salt while hot, if desired. Allow to rest 2–3 minutes so filling firms slightly before serving with lemon wedges.