Combine warm water, yeast, and a pinch of sugar in the large bowl of stand mixer and let sit around 5 min. until the yeast begins to foam.
Stir in warm milk, sugar, salt, vanilla, eggs, and oil. Add in flour, mixing, until dough is no longer sticky, using around 5 - 6 cups of flour. Mix with dough hook in stand mixer until the dough is smooth, and elastic and a sticky dough forms. Remove the dough from the bowl, and form it into a large ball. Oil a large mixing bowl and put the ball of dough inside the large greased bowl to rise, covered with greased plastic wrap, in a warm area, until the dough has doubled in size. This usually takes about an hour.
Punch down the dough mixture and knead the dough back into shape. Divide the dough into small pieces, about egg sized portions and roll out with a rolling pin on a lightly floured surface or stretch with your hands into an oval dough disk shape. The dough should be about ¼ inch thick. Cover so the dough doesn't dry out while you finish shaping the rest.
Heat the oil in a deep fryer to 375 degrees F (190 degrees C).
In a shallow dish or plate, combine 2 cups of white sugar with cinnamon to make the cinnamon sugar topping.
Fry the dough pieces in the hot oil, one at a time, for a few minutes per side, until golden brown. As soon as the fried dough pieces are removed from the fryer drain excess oil on a paper towel-lined plate. While still warm, coat the deep-fried bread dough in cinnamon sugar mixture, pressing it in and shaking to remove excess. These are best enjoyed fresh the day you make them.