You might find it unusual that as a monk I'm not a staunch defender of culinary tradition, and in the case of tsourecki I take any number of liberties. The traditional flavorings for this Greek treat are mastic (a spice made from resin which is dried and then ground) and aromatic mahlab (made from ground seeds of a cherry native to Greece). If you want a really traditional version of this recipe, you can find it HERE.
My version of this sweet, rich bread uses orange and anise as flavorings. I omit the red eggs, but there are plenty in dough---five, to be exact, and one more used as a glaze. It also has a whole stick of butter and 3/4 cup of sugar, so it's a very rich dough. The dough is a bit sticky even after kneading, but resist the temptation to add more flour; things will get better after the first rise.