In a bowl, combine 1/2 cup warm water (around 110°F), 3/4 cup warm milk, 1 tbsp sugar, and 2 tsp yeast. Whisk briefly and let it sit for about 10 minutes, until it becomes frothy.

In the bowl of a stand mixer, add 5 1/2 cups of flour (spooned and leveled with a knife), 1/2 tsp salt, 1/2 cup sugar, the frothy yeast mixture, and 5 large eggs. Attach the dough hook and mix everything together on medium-high speed.

Once the dough begins to come together, add 1/2 cup of softened unsalted butter. Continue mixing on medium-high speed for about 8 minutes, or until the dough is smooth, elastic, and no longer sticks to the sides of the mixer.

Transfer the dough to a greased bowl, covering it with a kitchen towel or plastic wrap. Let it rise in a warm place for about 1 hour, or until it doubles in size. (To speed up the process, I like to use the "proof" setting on my oven.)

After the dough has risen, punch it down to release the air. Reshape it and let it rise again for about an hour, or until it doubles in size.

Roll, Cut, and Proof the Donuts

Remove the dough from the bowl and place it on a well-floured surface. Dust the top with more flour and roll it out with a rolling pin to a thickness of about 3/4 inch, creating a rectangle approximately 15x17 inches. Use a pizza cutter to cut out 12 donut bars and transfer them to a flour-dusted baking sheet. Let them rise for an additional 30 minutes.

Pour about 2 inches of corn or vegetable oil into a heavy-bottomed pot. Heat the oil to 360-375°F, using an instant-read thermometer to check the temperature. Fry the donuts, cooking each side for a few minutes or until golden brown. Transfer the donuts to a baking sheet lined with paper towels to absorb excess oil. Let them cool completely.

Make the Maple Glaze and Dip

To make the glaze, melt 1/4 cup unsalted butter in a saucepan over medium heat. Add 1/2 cup brown sugar, 3 tbsp milk, and 1 tbsp corn syrup, and let the mixture come to a simmer. Once simmering, turn off the heat and stir in 2 tsp maple extract and 2 cups powdered sugar until smooth.

Once the donuts have cooled, dip them into the maple glaze and place them on a cooling rack to set. Enjoy!