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In the bowl of a stand mixer, combine the yeast and warm water, then stir to dissolve.
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Add the flour, milk, butter, egg yolks and sugar to the bowl and mix on low speed until everything is combined. Turn speed to medium and mix for about 3-4 minutes until the dough is smooth and lump free.
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Lay out a large silicone mat on the counter or dust work surface with flour. Knead dough into a ball shape. Coat a large bowl with some olive oil and transfer dough to bowl. Cover with a clean towel and let rise until doubled in size, about 1 hour.
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Once the dough has risen, punch it down. Roll the dough out on the prepared work surface to about a 1/4" thick then cut into doughnuts using a doughnut cutter. Repeat until all the pieces have been cut. Cover and allow the dough to rest for about 15-20 minutes.
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Heat oil on medium-high heat in a large pot or dutch oven until it has reached 375 degrees (I used a candy thermometer). You can also test if it's ready using the tip of wooden chopsticks or a wooden spoon.
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Gently place a couple of the doughnuts at a time into the hot oil. When they start to rise and turn golden, flip them over immediately using tongs or a wooden spoon (it should take less than a minute).
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The second side will turn golden very quickly and faster than the first side.
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Immediately transfer the fully fried doughnuts to paper towels to blot excess oil.
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Continue with the remaining doughnuts until everything is fried.
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To make the chocolate glaze: In a medium saucepan over medium heat, combine the butter and milk over medium-high heat, stirring until smooth. Turn the heat to low and add the chocolate, whisking until melted. Turn off the heat and add vanilla and corn syrup, whisking until smooth. Gently stir in the powdered sugar and whisk until smooth.
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Quickly dip the donuts into the glaze before it begins to set Allow to dry slightly and dunk again for a thicker glaze and top evenly with sprinkles. Place donuts on a wire rack for the excess glaze to fall and allow glaze to set on doughnuts for 30 minutes before serving.