Mix together warm water, yeast, and 1 pinch white sugar in a large bowl; let sit until creamy, about 5 minutes.

Grease a separate large bowl and set it aside.

Stir warm milk, eggs, vegetable oil, white sugar, salt, and vanilla into yeast mixture until sugar is dissolved. Add 2 1/2 cups flour until no dry spots remain and knead in remaining flour until smooth and elastic, about 10 minutes.

Form dough into a ball, place into prepared bowl, cover with a towel, and let rise in a warm place until doubled in volume, about 1 hour.

Punch down dough and knead briefly. Pinch off pieces, shaping them into ovals about 1/4-inch thick. Cover with a dish towel.

Heat oil in a deep fryer or pan to 375°F (190°C).

Make cinnamon sugar: Mix 2 cups white sugar and cinnamon in a dish.

Fry shaped dough in batches, about 1-2 minutes per side, until golden brown. Remove and drain on paper towels.