Whisk the dry ingredients: In a medium bowl, whisk flour, ginger, cinnamon, cloves, nutmeg, baking soda, and salt. Set aside.
Cream butter and sugar: In a large bowl, beat the softened butter and brown sugar until fluffy and light, about 2 minutes.
Scrape the bowl as needed.
Add wet ingredients: Mix in the molasses, egg, and vanilla until smooth. The mixture may look slightly curdled—this is normal.
Combine dough: Add the dry ingredients to the wet in two additions. Mix on low until a soft dough forms.
Do not overmix.
Chill: Divide dough in half, flatten into discs, wrap, and chill for at least 1 hour. Chilled dough is easier to roll and helps cookies hold their shape.
Preheat the air fryer: Heat to 325°F (165°C) for 3–4 minutes. Lightly oil or line the basket with a perforated parchment liner to prevent sticking.
Roll and cut: On a lightly floured surface, roll one disc to 1/4 inch thick.
Cut shapes with cookie cutters, then reroll scraps as needed.
Load the basket: Arrange cookies in a single layer in the basket, leaving a little space between them. Work in batches.
Air fry: Cook for 5–7 minutes at 325°F. Cookies are done when the edges are set and lightly browned.
Centers will firm as they cool.
Cool completely: Transfer to a rack. Let cool before icing, or the icing will melt.
Make the icing (optional): Stir powdered sugar, milk, and vanilla until smooth and pipeable. Adjust thickness with more sugar or milk.
Decorate: Pipe outlines, add buttons and smiles, or drizzle for simple designs.
Let icing set before storing.