Fill a medium heavy-bottomed saucepan with 2–3 inches of vegetable or canola oil. Heat oil over medium heat until it reaches 350°F (175°C). Use a frying thermometer to monitor the temperature carefully.
In a large bowl, whisk together flour, sugar, baking powder, and salt until fully combined.
Grate the cold butter into the flour mixture using a box grater. Stir gently until incorporated. Small butter pieces should still remain.
Pour in the milk and stir gently until the dough begins to come together.
Transfer dough onto a floured surface and knead gently until a cohesive dough forms. If the dough feels sticky, lightly add more flour until manageable.
Divide the dough into approximately 1½ tablespoon portions and roll into smooth balls.
In a small bowl, combine the cinnamon and sugar for rolling.
Line a plate or baking sheet with paper towels.
Once the oil reaches 350°F, carefully lower 2–3 dough balls into the oil using a slotted spoon.
Fry the Fried Donut Holes No Yeast for about 90 seconds, turning halfway through cooking until evenly golden brown.
Remove donut holes and place them on paper towels for about 1 minute.
Roll warm donut holes in the cinnamon sugar mixture until fully coated.
Repeat with remaining dough, allowing the oil to return to temperature between batches.