Add water and milk, stir, and bring to a boil. Reduce flame and simmer millet and carrots over low heat for about 20 minutes or until millet absorbs all the liquid and becomes soft. Stir occasionally to prevent burning. Remove from flame.
Mix in the butter and let the mixture cool slightly.
Whisk the eggs lightly with a fork; add cheese, chives, salt and pepper, mix. Blend the mixture into the slightly cooled millet.
Sprinkle a phyllo pastry sheet with the mixture of hot water and oil, lay another sheet onto it, and sprinkle again.
Distribute evenly one third of the filling onto the prepared sheets, roll into strudel. Repeat the process with the rest of the sheets. The amount is enough for 3 rolls.
Place the strudels in a greased tin.
Brush each roll with melted butter. Bake in the oven at 180˚C for 30 minutes until golden in colour.
Leave the strudel to cool slightly before cutting. Serve with yogurt.