Combine the mashed bananas, eggs, vanilla extract, and vegetable oil in a large mixing bowl. Whisk until smooth and well integrated.
In a separate bowl, whisk together the flour, baking soda, cinnamon, salt, and sugar. Gradually add the dry ingredients to the banana mixture, stirring until just combined and no streaks remain.
Heat vegetable oil in a deep fryer or heavy-bottomed pot to 350°F (175°C). Use a thermometer to monitor the temperature for precise frying.
Scoop the batter using a spoon or ice cream scoop, gently dropping portions into the hot oil. Fry for about 2-3 minutes on each side, turning with a slotted spoon, until the donuts are golden brown and risen.
Use a slotted spoon to remove the donuts from the oil once they reach a golden color and register 180°F internally. Transfer to a cooling rack lined with paper towels to drain excess oil.
Allow the donuts to cool slightly before serving. Optional: dust with powdered sugar or cinnamon sugar for extra flavor and presentation.