Place the milk in a large mixing bowl and warm it in the microwave until just lukewarm. With a wooden spoon, stir in the yeast, sugar and salt and until completely dissolved. Stir in the flour, butter, eggs and flavoring and mix well.
Knead dough just until smooth and then gather into a round. Place the dough in a lightly oiled bowl and cover with plastic wrap. Place in the refrigerator until chilled - three or four hours or overnight.
Remove the dough from the refrigerator and roll it on an a lightly floured surface until it is about 1/2 inch thick. You can cut the dough into any shape you wish - diamonds are popular in France.
Heat the oil in a sturdy pot (or use a deep fat fryer if you have one) until it is 360° F. Drop the beignets in the hot oil and cook in small batches, using metal tongs to turn them occasionally. They should take two to three minutes to be golden brown and puffy.
Remove the beignets with the tongs and place them on folded paper towels to drain the excess oil. Sprinkle with powdered sugar if you wish and enjoy your beignets hot.
Makes a couple dozen beignets, but it depends on how you cut them!