In a small bowl, dissolve yeast in warm water. Let stand for 5 minutes until foamy.
In a large bowl, combine yeast mixture, sugar, milk, shortening, salt, and eggs. Beat until smooth. Gradually add flour, mixing until a soft dough forms.
Turn dough out onto a lightly floured surface and knead for 5-7 minutes, or until smooth and elastic. Place dough in a greased bowl, turning to coat. Cover and let rise in a warm place for 1-1.5 hours, or until doubled in size.
Punch down dough and turn out onto a lightly floured surface. Roll dough out to 0.5-inch thickness. Cut out donuts using a donut cutter or two different-sized round cutters.
Place donuts on a baking sheet lined with parchment paper. Cover and let rise for 30 minutes.
Heat oil in a large pot or deep fryer to 350°F (175°C). Carefully drop donuts into hot oil, a few at a time. Fry for 1-2 minutes per side, or until golden brown.
Remove donuts from oil and place on a wire rack to drain.
In a shallow bowl, combine sugar and cinnamon. Dip warm donuts in melted butter, then coat in cinnamon sugar mixture.
Serve immediately and enjoy!
Notes
These donuts are best served fresh. You can store leftovers in an airtight container at room temperature for up to 2 days.