In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt until evenly combined.
In a separate bowl, whisk together the melted butter, eggs, milk, vanilla extract, and sour cream until smooth and well blended. Pour the wet ingredients into the dry ingredients and stir gently with a spatula until just combined.
Do not overmix - a few small lumps are perfectly fine. The sour cream keeps this cake incredibly moist.
Grease a 6-inch or 7-inch round cake pan that fits inside your air fryer. Line the bottom with a circle of parchment paper and grease the parchment as well. Pour the batter into the prepared pan and smooth the top with the back of a spoon.
Set the air fryer to 310 degrees F. Place the cake pan in the air fryer basket and bake for 25 to 30 minutes, until the top is golden and a toothpick inserted in the center comes out clean.
If the top begins browning too quickly, loosely cover with a small piece of foil for the remaining time.
Remove the pan from the air fryer and let the cake cool in the pan for 10 minutes. Run a knife around the edges, then carefully invert onto a wire rack to cool completely.
While the cake cools, whisk together the powdered sugar, milk, and vanilla extract until smooth and pourable. If the glaze is too thick, add milk a few drops at a time. If too thin, add a bit more powdered sugar.
Drizzle the vanilla glaze over the top of the cooled cake, letting it drip naturally down the sides. Allow the glaze to set for about 5 minutes before slicing and serving.