Knead a soft dough from the ingredients for it, divide it into 5 balls and let them rise for 30-40 min. Roll out the 1st ball into a sheet about 1/2″ (1 cm) thick. Smear it with margarine and/or lard and put it aside.
Roll out the next 2 sheets the same way, placing the 2nd on top of the 1st, and the 3rd on top of the 2nd. On the 3rd greased sheet, crumble part of the feta cheese and cover with the remaining 2 sheets, which you've greased like the first few.
Grab the 5 sheets together, fold them in 2 and leave them to sit for 15 min. Roll out the 5 sheet layer to a thickness of 3/4″ (2 cm), smear it one final time and put the rest of the feta cheese on top.
Wrap it into a roll and cut it into 1" (2.5 cm) strips. Arrange them in a greased oven dish, facing up. Leave them to rise a little bit more and smear with the beaten yolk mixed with a few drops of oil.
Bake the tutmanik in a preheated 410°F (210 °C) oven for 30-40 min. until it's well baked. After you take it out, sprinkle it with cold water, cover with paper and then with a towel and leave it to smother and soften.