Prepare Yeast: Mix yeast and warm water; let sit for 10 mins until foamy.
Make Dough: In a large bowl, combine warm milk, shortening, sugar, salt, and vanilla. Add 1 cup flour; mix. Add yeast mix, water, and eggs. Slowly add remaining flour to make soft dough.
Knead: Knead dough on floured surface for 5-10 mins. Place in greased bowl, cover, and chill 3 hours or overnight.
Roll & Cut: Roll dough to 1/3 inch thick. Cut with donut cutter (or use cup and bottle cap).
Rise: Place donuts on parchment, cover with cloth, and let rise 1 hour until doubled.
Fry: Heat oil in pot to 350°F. Fry donuts 2 mins per side until golden brown. Cool on wire rack.
Vanilla Glaze: Mix powdered sugar, milk, and vanilla. Dip donuts and let dry on rack.
Chocolate Glaze: In saucepan, melt butter with milk, corn syrup, and vanilla. Remove from heat, add chocolate chips, stir until melted. Mix in powdered sugar.
Optional: Fill with jam using piping bag or shake in cinnamon sugar.