Heat the milk in a small saucepan on medium heat, until bubbles start to appear across the surface. Stir the milk occasionally, and do not let it come to a boil. Add the butter to the pot. Remove the pot from the heat and let it cool to 105 degrees.
Add the following ingredients to your bread machine, in the order suggested by the manufacturer: the cooled milk and butter, flour, yeast, salt, sugar, egg, and vanilla.
Process on the dough cycle. Mine takes one hour and fifty minutes.
Preheat the oven to 400 degrees.
On a floured board, roll the finished dough out into a quarter inch thick rectangle. Cut the dough into two inch squares. You'll have about 28 of them.
Place the dough squares on two parchment lined baking sheets, with about two inches of space between each beignet. Bake for 12 minutes, rotating the pans between racks after six minutes. They should be light brown. Place them on a wire rack and sprinkle with the confectioner's sugar.
To make the strawberry sauce: In a three quart saucepan over low heat, cook the strawberries, sugar, cornstarch and water on medium heat for five minutes, or until the mixture thickens. Serve with the beignets.