In the bowl of an electric stand mixer, whisk together yeast, warm water, and 1/2 tsp of the sugar. Let rest for 5-10 minutes. Add in evaporated milk, remaining granulated sugar, salt, 1/4 cup shortening, egg, egg yolk, and vanilla.

Add half of the flour and use the whisk attachment to blend until smooth. Switch to the hook attachment, slowly add remaining flour, and knead on low speed until smooth and elastic, about 4-5 minutes, adding additional flour as needed.

Transfer dough to a lightly oiled bowl, cover with plastic wrap, and let rise in a warm place until doubled in size, about 1 1/2 hours.

Punch the dough down and roll it into an even layer onto a floured surface to slightly less than 1/2-inch thickness.

Cut into doughnut shapes using a doughnut cutter or two round circle cutters. Cover and let rise until doubled, about 30-40 minutes.

Heat shortening in a cast iron dutch oven to 360 degrees.

Meanwhile, prepare the glaze by mixing all of the glaze ingredients in a shallow dish to ensure it is fairly thick.

Carefully transfer the doughnuts to the oil and fry until golden on the bottom, then flip using a wooden chopstick and fry until golden brown on the opposite side.

Transfer to a wire rack and allow to cool for 1-2 minutes, then dip the top half in glaze while still warm and return to the wire rack to allow glaze to set at room temperature.