The Best Glazed Yeast Doughnuts

• Add the warm water, ½ teaspoon of sugar, and yeast to a small bowl and stir just until combined. Let sit for 10 minutes or until bubbly and frothy. (If the mixture doesn't bubble, your yeast has probably gone bad and you will need to start over with new yeast.)
• While the yeast is proofing, combine the additional ⅓ cup of sugar, warm milk, melted butter, eggs, vanilla, and salt in the bowl of the stand mixer. Whisk until fully combined and then add the yeast mixture once frothy.
• Start mixing with the hook dough attachment on low and gradually add the flour, one cup at a time, until all 5 cups have been added. Increase the speed to around medium and let the mixer knead the dough for around 10 minutes or until a smooth, soft dough forms. It's okay if the dough is still a little sticky. Form the dough into a smooth ball and place it in a well-oiled bowl, oiling the top of the dough as well. Cover with plastic wrap and let rise in a warm place for 1 hour until doubled or more in size.
• When the dough is rising, prepare 3 or 4 large baking sheets with parchment paper or wax paper; these are to place the doughnuts on to rise. Once risen, punch down the dough to deflate. Transfer to a lightly floured counter and roll out to about ½ inch in thickness. Cut out doughnuts using a floured doughnut cutter or two cookie cutters. Place doughnuts on the prepared pans, leaving room between them to rise. Cover the pans with plastic wrap and let rise for 30 minutes.
• While the doughnuts are rising, start heating your oil to 350℉ in a large dutch oven or a heavy pot. Prepare the glaze (recipe below) so that it's ready to glaze the doughnuts while they are still hot. Prepare a baking sheet or plate with some paper towel to place the doughnut on as soon as they come out of frying to absorb excess oil. Prepare a wire rack to place the doughnuts on after glazing with a parchment paper-lined baking sheet underneath to catch excess glaze that drips down.
• Once the doughnuts have risen and your oil has reached 350℉, it's time to start frying! Fry as many doughnuts as you can fit at one time in your dutch oven or pot without crowding them. Try to maintain an oil temperature of 350℉ and adjust the heat as necessary. Fry until golden brown on the first side and then flip using a fork. The time for each side really varies, but you will figure it out as you go.
• Remove the doughnuts from the oil with a fork onto your paper towel-lined pan and allow the grease to soak up for a few minutes before glazing them in the still-warm glaze. Dunk one side and flip and dunk the other. Work quickly and be careful not to burn yourself, the doughnuts will still be very hot. Place on the wire rack to let the excess glaze drip off.
• Repeat this process until all the doughnuts and doughnut holes are fried and glazed. I usually fry all the doughnuts first and then do the doughnut holes at the end. Enjoy!

To make the Glaze:

• In a small saucepan over medium heat, add the granulated sugar, milk, butter, and salt. Bring to a boil for 2 minutes, stirring constantly. Remove from the heat and add the vanilla extract before gradually adding the powdered sugar and whisking well until fully combined and no lumps remain. Transfer to a medium-sized bowl.