1. Heat oil to 350°F. In a bowl, whisk together flour, sugar, baking powder, and salt.
2. In a separate bowl, whisk together milk, brewed coffee, egg, melted butter, and vanilla extract, then stir into the dry ingredients until a smooth, thick batter forms.
3. Drop small spoonfuls of batter into the hot oil and fry for 2–3 minutes, turning occasionally, until golden brown on all sides. Remove and drain on a wire rack over a sheet tray.
4. In a separate bowl, whisk together powdered sugar, brewed coffee, and vanilla extract until a smooth, glossy glaze forms.
5. Pour the glaze generously over the donut holes on the sheet tray. Let set for a few minutes until shiny and slightly firm, then serve.