Combine Ingredients: In a medium saucepan, combine the water, milk, butter, 1 teaspoon of sugar, and the salt. Heat the mixture over medium heat, stirring occasionally, until it begins to boil. Once boiling, remove the pan from the heat.
Incorporate the Flour: Stir in the flour using a wooden spoon until it forms a thick, smooth dough. Mix until no dry flour remains, and the dough pulls away from the sides of the pan.
Cook the Dough: Place the pan back over medium heat and stir the dough constantly for 1½ to 2 minutes. This step helps reduce excess moisture and ensures the flour is cooked. The dough should be smooth and leave a thin film on the bottom of the pan.
Cool and Beat the Dough: Transfer the dough to the bowl of a stand mixer fitted with a whisk attachment, or use a large mixing bowl and a hand mixer. Beat the dough on medium speed for about 1 minute to cool it slightly. Add the eggs one at a time, beating thoroughly after each addition. Once all the eggs are added, continue beating until the dough is smooth and forms a ribbon-like consistency when lifted. Set aside.
Prepare Cinnamon Sugar: In a separate bowl, mix the remaining ½ cup of sugar with the ground cinnamon. Line a large plate with paper towels to use for draining the donuts after frying.
Heat the Oil: In a deep pot or Dutch oven, pour about 1½ inches of oil and heat it to 375°F. To check the temperature, use a clip-on thermometer for accuracy.
Fry the Donuts: Using a teaspoon or small scoop, carefully drop spoonfuls of dough into the hot oil. Avoid overcrowding the pot to maintain the oil temperature. Fry each batch for about 4 minutes, flipping the donuts halfway through to ensure even browning. Once golden, use a slotted spoon to transfer the donuts to the paper towel-lined plate to drain excess oil.
Coat with Cinnamon Sugar: While the donuts are still warm, roll them in the cinnamon-sugar mixture until evenly coated. Repeat the process with the remaining dough.
Serve and Enjoy: Transfer the coated donut holes to a serving dish and enjoy them fresh and warm, or allow them to cool to room temperature before serving.