Combine water with 1 teaspoon sugar and yeast and let the mixture sit for 10 minutes or until the yeast has bloomed.
Whisk together eggs with evaporated milk and melted butter. Measure 2 cups of bread flour in a large bowl and add the egg mixture, yeast mixture, salt, and dry milk powder. Mix until well combined, slowly adding the remaining 1 ½ cups flour. Knead dough until smooth, about 5-7 minutes. Cover with plastic wrap and let rise in a warm place for 2 hours or until doubled in size.
Preheat oil in a deep fryer to 350 degrees F.
Mix the powdered sugar with matcha in a medium bowl. Set aside.
Punch down the dough. Dust a clean work counter with flour and roll out the dough into 2x2 inch squares, about ¼ inch thick. Carefully deep fry the dough in batches, flipping constantly until they become golden brown. Remove beignets with a slotted spoon onto a paper towel-lined plate. Repeat with remaining dough. Dust generous amount of matcha sugar onto the beignets and serve while warm.