In a mixing bowl, combine flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk together buttermilk, egg, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Heat oil in a deep fryer or heavy pot to 350°F (175°C).
Use a piping bag or a spoon to fill a mini donut pan with batter.
Carefully place the filled pan into the hot oil, cooking until golden brown (about 1-2 minutes per side).
Remove the donuts from the oil and place them on paper towels to drain excess oil.
Let them cool slightly before glazing or topping.
For glazing, mix powdered sugar with a little milk until smooth and dip the donuts.
Add sprinkles or toppings as desired before serving.