For the donuts: Add the yeast, granulated sugar, milk, flour, salt, eggs, egg yolks and shortening to a mixing bowl (in the order listed). Mix on low speed with a dough hook attachment until the dough is very smooth and elastic and makes a slapping sound against the sides of the bowl, 25 to 30 minutes. Scrape the dough into a greased container, cover and refrigerate overnight.
Two hours before you want to roll the dough, remove it from the refrigerator to temper. Dump the dough onto a floured work surface and roll to 1/2-inch thick. Cut the donuts using a donut cutter and place on a tray with parchment paper that's been greased and floured. Cover with plastic wrap and let proof for 1 hour.
Turn on your deep fryer to 325 degrees F. When they are ready to fry, the donuts will be very light and airy feeling; they should barely hold their shape when handled. Fry for 2 minutes per side. Drain on a wire rack or paper towels.
For the butter crunch: First, make the toffee. Heat the butter, granulated sugar and salt in a nonreactive pan on medium-high heat, stirring constantly with a wooden spoon. Cook until deep golden or camel colored. Pour onto a silicone baking mat or sprayed parchment paper on a tray and let cool completely. It will be very hard and shatter if you tap it. Then, grind the toffee in a food processor with the toasted pecans. It should be uniformly finely ground.
For the glaze: Whisk the milk and confectioners' sugar together until perfectly smooth. Strain to remove any lumps.
To assemble: Dunk the cooled donuts in the glaze. Let it drain for 1 minute. Roll the donut in the butter crunch, making sure to completely cover all sides.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of Sarah Sanneh, Pies 'n' Thighs, Brooklyn, NY