Sprinkle yeast over warm water and let stand five minutes or until foamy.
In a large bowl, mix together the yeast mixture, milk, sugar, salt, eggs, shortening and two cups flour. Mix for a few minutes at low speed.
Beat in remaining flour, 1/2 cup at a time, until the dough no longer sticks to the bowl. Knead for about five minutes or until smooth and elastic.
Place the dough in a greased bowl and cover. Let rise in a warm place until doubled in bulk, about an hour or a bit longer.
Turn the dough onto a floured surface and gently roll out to 1/2-inch thickness. Cut into circles. Let rise again until doubled in bulk.
Heat 4 cups of oil in a deep fryer or large pot to 350. Carefully slide doughnuts into hot oil using a wide spatula. Turn the doughnuts over as they rise to the surface. Doughnuts are ready when both sides are golden brown.
Fill with 1 T jelly using a pastry injector, or by cutting a small slit in the side of the doughnut and inserting the jelly with a baby spoon. Close tightly; roll in confectioners' sugar.