In a large bowl, beat the room-temperature butter and sugar on medium-high for 4 to 5 minutes, until pale and fluffy. Scrape the bowl down halfway through. This step is the only leavening in the recipe, so don't rush it.
Add the eggs one at a time, beating each one in fully before adding the next. If the batter looks separated, add a spoonful of the flour to bring it back together.
Add the flour in three additions on low speed, mixing only until the last streaks disappear.
Grease three mini loaf pans well and fill each about two-thirds full. Smooth the tops.
Set the pans in the air fryer basket, leaving space around them for air to circulate. Air fry at 320°F for 20 minutes.
Insert a toothpick into the center of a loaf. Moist crumbs mean it's done; wet batter means it needs more time. Add 5 minutes and check again, repeating until set.
Cool in the pans for 10 minutes, then turn out onto a wire rack and cool completely before slicing.