Add the mixture to the flour and knead a soft dough; add more flour if needed.
Place the dough in a lightly floured plastic bag and tie it. Put the bag in the fridge for 1 hour. You can store this dough in the fridge for several hours though.
Roll out the dough onto a floured counter (without kneading again) into a sheet 1/2″ (1 cm) thick. Smear the sheet with water using a brush, then cut it into squares.
Mix the finely grated feta cheese with the egg white, stir until homogeneous.
With a teaspoon, place filling onto each square of dough and wrap up into a roll. Make sure they stick well once rolled up, so they don't unroll during frying.
Heat about 3 finger widths of oil in a narrow and deep container, lower the heat to low and place the shaped pirozhki in it (about 4-5 at a time).
Fry about 3-4 min. on all sides. Place the fried pirozhki onto paper towels to drain the excess oil.
Crunchy on the outside, soft and fluffy on the inside!