In a large bowl, dissolve yeast in warm water. Add sugar, shortening, salt, and milk. Mix well.

Gradually add flour until a soft dough forms. Knead for 5-7 minutes.

Place dough in a greased bowl, turning to coat. Cover and let rise in a warm place for about 1 hour, or until doubled.

Punch down dough and roll out to 1/2 inch thickness. Cut out donut shapes with a donut cutter or cookie cutter.

Place donuts on a baking sheet lined with parchment paper. Cover and let rise for another 30 minutes.

Heat vegetable oil in a large pot or deep fryer to 350°F (175°C).

Carefully drop donuts into hot oil, a few at a time, and fry for 1-2 minutes per side, or until golden brown.

Remove donuts and place on a wire rack to cool.

In a medium bowl, whisk together melted butter, powdered sugar, cocoa powder, milk, and vanilla extract until smooth. Add more milk if needed to reach desired consistency.

Dip the tops of cooled donuts into the chocolate frosting, allowing excess to drip off.

Place frosted donuts back on the wire rack to allow the frosting to set. Add sprinkles or other toppings, if desired.

Serve and enjoy!