Begin by heating the oil in a medium-sized, heavy-bottomed saucepan over medium heat. Fill it with 2-3 inches (5-7 cm) of oil and use a candy or frying thermometer to monitor the temperature, aiming for 350°F (175°C). This process may take about 20 minutes or longer.

In a large bowl, whisk together the flour, 3 tablespoons of sugar, baking powder, and salt until well combined.

Grate the very cold butter into small pieces using a box grater and add it to the flour mixture. Stir until the butter is well incorporated, though some visible pieces should remain. If you don't have a box grater, you can use a pastry cutter to mix the butter into the dry ingredients until the mixture resembles coarse crumbs.

Pour in the milk and gently stir until all the ingredients come together to form a dough that clings together.

Transfer the dough to a well-floured surface and knead it gently until it forms a cohesive ball. If the dough is too sticky, gradually work in more flour until it becomes smooth and manageable.

Divide the dough into pieces of about 1 ½ tablespoons each and roll them into smooth, tight balls. Set these aside.

In a small dish, mix together the cinnamon and remaining sugar to create a cinnamon-sugar mixture for rolling the donut holes. Set this aside as well.

Prepare a large plate or baking sheet by lining it generously with paper towels to absorb excess oil from the cooked donut holes.

Once the oil has reached 350°F, carefully fry the donut holes in batches of 2-3 at a time. Use a slotted spoon to lower them into the oil gently to avoid splashing.

Fry the donut holes for about 90 seconds, turning them halfway through to ensure they are evenly golden brown.

Using a slotted spoon, remove the donut holes from the oil and place them on the paper towel-lined plate. Let them cool for about a minute or until they are no longer too hot to handle.

Transfer the warm donut holes to the cinnamon-sugar mixture and roll them until they are fully coated.

Make sure to allow the oil to return to 350°F (175°C) between batches and repeat the frying and rolling process until all donut holes are cooked.