Place the sugar in a large bowl and pour the warm water on top.

Sprinkle the yeast over the surface of the water and allow it to dissolve (approx. 5 minutes).

Stir in the milk, melted butter, and egg until incorporated.

Add the flour, cinnamon, and salt, mixing together until a sticky dough forms.

Knead the dough until smooth and elastic (approx. 2 minutes).

Cover the bowl with plastic wrap and allow the dough to rise in a warm place until doubled in bulk (approx. 1 hour).

Punch down the dough and knead/chop in the apple until incorporated, then divide the dough into 12 equal portions.

Chop each portion, forming it into a rough disc shape, then place each uncooked apple fritter on a square of parchment on a sheet pan.

Cover the pan lightly with a lightly greased sheet of plastic wrap and allow the fritters to rise and double a second time (approx. 1 hour).

Heat a large pot of about 2 inches of oil to between 325 and 375 degrees F.

Gently place a few fritters at a time in the hot oil, removing the parchment squares as the fritters fry.

Fry until golden on each side, then drain on paper towels.

Stir the powdered sugar, milk, and vanilla together until smooth.

Dip each fritter in the glaze when cool enough to handle.