Mix together the flour, sugar, baking powder, cinnamon, and salt in a mixing dish.
Whisk the eggs, milk, melted butter, and vanilla extract in a separate basin.Stirring constantly, gradually incorporate the wet components into the dry ingredients until a soft dough forms.
Roll out the dough to a thickness of about 1/2 inch on a surface dusted with flour.Cut out doughnut shapes with a donut cutter or cookie cutters.
In a big pot or deep fryer, heat the oil to 350°F (175°C).
The donuts should be carefully added to the hot oil and fried for one to two minutes on each side, or until golden brown.
After removing the donuts from the oil with a slotted spoon or spider strainer, lay them out on paper towels to absorb any remaining oil.
Let the doughnuts cool slightly before glazing or dusting with powdered sugar, cinnamon sugar, or your favorite toppings.
Serve and enjoy these freshly made donuts with a cup of coffee or tea!