Combine flour, yeast, sugar, and salt in a mixing bowl.

Mix for 1 minute.

Add warm water and half of the beaten egg to the bowl.

Mix the ingredients together.

Add butter until well combined.

Knead the dough by hand until it becomes smooth and elastic (approximately 10 minutes).

Cover the dough and let it rise in a warm area for around 30 minutes.

Punch down the risen dough.

Divide the dough into 8 equal round balls and allow them to rise for 10 minutes.

Roll out each ball with a rolling pin into a thin disk (about 5 inches in diameter and 1/4 inch thick).

Heat olive oil in a pan over medium-high heat, then add chopped garlic and mix.

Add chopped red onion, crumbled smoked salmon, and mashed potatoes to the pan.

Mix the filling ingredients until the onion softens and everything is heated through.

Season the filling with black pepper and salt.

Mix the filling well to combine the flavors.

Place a tablespoon of the filling mixture in the middle of each dough disk.

Fold the edges of the disk in three places to cover the filling, creating a bun shape.

Place the filled fish buns on a greased baking tray and let them rise for 35 minutes.

Brush the remaining beaten egg over the tops of the fish buns.

Sprinkle sesame seeds on top of the brushed egg wash.

Bake in a preheated oven at 200°C (392°F) for 20 minutes, or until the buns are golden brown.

Serve the baked fish buns with tomato sauce for dipping.

Enjoy your homemade fish buns.