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In a 2 quart saucepan heat the milk, butter, and salt, until it comes to a boil.
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Remove from the heat and with a wooden spoon vigorously stir in the flour all at once until mixture forms a ball, and leaves the side of the pan.
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Add the eggs, one at a time.
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Beat after each addition until smooth. Stir in crumbled feta and cool slightly.
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Preheat oven to 350 degrees.
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Lightly grease a sheet pan or line with parchment paper.
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Drop batter in small 11/2 inch balls.
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Make the egg wash by beating the 1 egg with 1 tablespoon water or milk. Brush on balls with wash.
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Bake for 15-20 minutes until golden brown. Transfer to a wire rack to cool.