In a small bowl, soften yeast in warm water; set aside for 10 minutes.
In large bowl, combine milk, shortening, sugar, salt and vanilla and cool to lukewarm.
Add 1 cup of the flour and beat well; beat in yeast, water and eggs.
Add remaining flour and make soft dough; knead well.
Place in greased bowl; cover and chill 3 hours, or overnight.
If it raises in refrigerator, punch it down.
Turn on lightly floured surface; roll 1/3 inch thick.
Cut with floured donut cutter.
Let the donuts rise about an hour or until they double in size.
Fry in canola or sunflower oil, at 350°F, about 2 minutes per side or until brown.
Turn only once or the doughnuts will soak up too much oil.
Drain on a wire rack.
Cool completely before attempting to glaze.
