In a mixing bowl, whisk together flour, sugar, baking powder, and salt.

In another bowl, combine egg, milk, melted butter, and vanilla extract.

Gradually add the wet ingredients to the dry ingredients, mixing until just combined.

Heat oil in a frying pan to 350°F (175°C).

Use a donut cutter to cut out donuts from the batter.

Fry the donuts in batches until golden brown, about 2-3 minutes per side.

Remove and place on a cooling rack to drain excess oil.

In a bowl, whisk together powdered sugar, milk, and vanilla until smooth.

For chocolate glaze, mix in cocoa powder until well combined.

Dip each donut into the glaze, allowing excess to drip off.

Sprinkle with toppings as desired.

Serve immediately and enjoy!