Preheat oven to 350°F (175°C) and lightly grease a donut pan.
In a bowl, whisk flour, sugar, baking powder, baking soda, and salt.
In another bowl, combine buttermilk, egg, melted butter, lime juice, zest, and vanilla.
Mix wet ingredients into dry until just combined.
Pipe or spoon batter into donut pan, filling each cavity about ¾ full.
Bake for 10–12 minutes or until golden and a toothpick comes out clean.
Let donuts cool for 5 minutes, then transfer to a wire rack.
For the glaze, whisk powdered sugar, lime juice, and zest until smooth.
Dip cooled donuts into glaze, let set, and serve.