In a bowl, add in the egg yolks, milk, and strong coffee, Whisk until incorporated.
In a medium saucepan, add in the sugar, salt, and cornstarch. Whisk until the cornstarch is thoroughly incorporated.
Pour about 3/4 cup of the egg and milk mixture into the saucepan and whisk until incorporated. Start with a small amount to avoid lumps.
Add the remaining egg and milk mixture and whisk to combine.
Add in the butter and turn heat on to medium. Whisk pretty steadily to avoid clumps and burning.
Once the mixture comes up to a boil, let it boil for 1 minute until it thickens. Whisk constantly while the custard is boiling.
Immediately run the custard through a fine mesh strainer into a bowl.
Cover with plastic wrap. Be sure that the plastic wrap sits on the top of the custard to avoid a skin. Place into the fridge to chill.
Dissolve yeast in the ¼ cup warm water. Add a teaspoon of sugar and stir. Let it sit for 10 minutes until foamy. This will mean your yeast is activated.
In a saucepan, add in the milk, shortening, sugar and salt. Turn on heat to medium/high. Let it come to almost a bubble. Once the milk starts to form bubbles on the outer edge, remove from the heat and let cool to luke warm.
Add the milk mixture, yeast, mashed potatoes, and beaten eggs into a large mixing bowl. Stir to combine.
Add in the 5 cups of flour and stir until most of the flour is incorporated. Remove the dough from the bowl onto a clean work surface and work in the rest of the dough. Knead the dough until smooth. It will be a soft dough.
Place 1 tablespoon of oil into a bowl. Add the dough and roll it into the oil to coat it. Cover with plastic wrap and place in a warm area until doubled. It will take about 1 hour and 30 minutes.
Lightly flour a clean surface. Turn the dough out onto the the floured surface and roll out to about ½ inch thickness. Cut with 3 or 4 inch round cookie cutter.
Place the cut out donuts onto two cookie sheets that have been greased with non-stick cooking spray. I normally lay a piece of parchment paper down onto the cookie sheet and then spray that with non-stick cooking spray. The parchment paper isn't necessary.
Cover the donuts with the plastic wrap and let it rise until doubled. This will take about 30 minutes.
While the donuts are rising for the second time, add the 3 cups of oil into a large saucepan and let it heat to 350 degrees.
Once the donuts are doubled and the oil is up to temperature, add 1 to 2 donuts into the oil. Let the donuts fry for about 2 minutes until golden brown. Flip and let fry for another minute to two minutes until that side is golden brown.
Remove from the oil and place on a wire rack to drain.
Place the granulated sugar and cinnamon in a storage bag or paper bag.
Toss the warm donuts into the cinnamon and sugar.
Add the # 230 Bismarck Metal Tip in a large disposable piping bag. Fill the bag with the coffee custard.
Pipe the custard into the center of the donuts. Fill until the centers of the donuts puff out slightly.