Combine the milk, yeast, and sugar in the bowl of a stand mixer fitted with the dough hook attachment. Whisk manually, and let sit for 5 minutes in order to activate the yeast.

Add the egg, and whisk in by hand. Add 400g of the flour to the bowl, along with the kosher salt. Knead on medium speed for 1 minute. Start adding the butter to the bowl, 1 tablespoon at a time. Let the butter incorporate into the dough before adding the next tablespoon. Then add the remaining 55g of flour. Knead for 5-6 minutes on medium speed. The dough should just clear the sides of the bowl but should be sticky and soft.

Remove the dough hook, and cover the bowl with plastic wrap or a clean kitchen towel. Allow the dough to rise at room temperature for 1-2 hours, or until the dough has doubled in size. The rate of the rise really depends on your room temperature. A warmer kitchen (70° and up) will help the dough rise faster.

Cut about 20 rectangular pieces of parchment paper, about 3"x4". Set aside.

Generously flour your work surface. Pour the risen dough out onto your prepared surface. Divide the dough into 75g pieces, about 20 pieces. Flour hands well, and gently stretch each piece of dough into a 12-inch long rope. Fold the dough in half, and twist it around itself, pinching the two ends together at the bottom.

Place each twist on a small piece of cut parchment paper. Place the prepared twists on a baking sheet, and cover loosely with a clear kitchen towel. Let them proof for 30 minutes at room temperature while your oil is heating up.

Heat 3 inches of oil in a heavy bottomed pot to 350° F. Use a candy thermometer to get the temperature just right. Gently lower the twists into the pot to fry with the parchment paper. Allow the doughnuts to sink, and just pull the parchment paper out and discard. Fry for 2-3 minutes on the first side, then flip the doughnuts with a chopstick, and fry for another 2-3 minutes until golden brown. Let the maple twist doughnuts drain on a baking sheet lined with a rack.

Make the glaze by combining the powdered sugar, milk, maple extract, and salt. Whisk well until you reach your desired consistency. Brush the doughnuts with the maple glaze, and let the glaze set for about 10-15 minutes. Enjoy right away!