In a non-stick skillet, melt butter over medium heat and cook shallot for 2 minutes or until softened and starting to brown.
In a bowl, beat eggs. Pour into skillet and cook, stirring gently, forming large curds from the outside edge of pan into the centre. Stir in cream cheese until melted. Remove from heat and stir in smoked salmon and chopped chives; set aside to cool.
Meanwhile, place one sheet of phyllo on work surface; brush with butter. Top with second sheet; brush with butter. Top with third sheet and brush with butter. Cut into 12 squares. Place 1 tablespoon of the filling in centre of each square. Bring up corners, pinching above filling to secure, twisting slightly to seal. Repeat with remaining phyllo and filling to make another 12 pouches.
Place pouches in single layer on a parchment paper-lined baking sheet.
Bake in the preheated oven for about 10 minutes or until golden. Let cool slightly before serving.