Dissolve yeast in warm water in a medium bowl, let rest for 10 minutes.

Add milk, sugar, salt, eggs, shortening or butter, and 2 cups flour.

Beat on low for 30 seconds, scraping bowl constantly. Beat on medium speed for 2 minutes, scraping bowl occasionally. Stir in remaining flour until smooth.

Cover and let rise until double, 45-90 minutes. (Dough is ready when indentation remains when touched.)

Turn dough onto floured surface; roll around lightly to coat with flour. Gently roll dough 1/2-inch thick with floured rolling pin.

Cut with floured doughnut cutter.

Place cut donuts on a parchment or baking mat lined baking sheet. Cover and let rise until double, 20-30 minutes.

While the cut doughnuts rise, make the creamy glaze - heat butter until melted. Remove from heat. Stir in powdered sugar and vanilla until smooth. Stir in water, 1 tablespoon at a time, until desired consistency.

Heat vegetable oil in deep cast iron skillet to 355 to 365 degrees F (use a thermometer here, it makes all the difference!).

Slide doughnuts into hot oil with wide spatula. Turn doughnuts as they rise to the surface. Fry until golden brown, about 1 minute on each side.

Remove carefully from oil; drain on a double layer of paper towels.

Dip the hot doughnuts into creamy glaze, then set on cooling rack set inside of a rimmed baking sheet to collect the drips.

Best enjoyed warm with friends.