Zest the orange and set aside, then juice it and measure out the juice. Grate the carrots into 1/8-inch shreds and set aside. Melt the butter and let it cool to room temperature—this prevents the eggs from cooking when mixed in. Measure out all dry ingredients (flour, cinnamon, nutmeg, salt) and combine them in a small bowl, whisking together to distribute the spices evenly. This dry mixture is ready to fold in later.
In a large mixing bowl, whisk together the brown sugar and cooled melted butter until well combined. The mixture should be smooth and homogeneous. Add the eggs one at a time, whisking well after each addition to create a light, emulsified base. This technique incorporates air into the batter, which helps the cake rise in the air fryer.
Add the orange juice and orange zest to the wet mixture from Step 2 and stir to combine. Fold in the dry ingredient mixture from Step 1 using a spatula, being careful not to overmix—fold gently until just combined. Finally, fold in the grated carrots and sultanas. I find that gentle folding preserves the tender crumb of the final cake, so resist the urge to stir vigorously.
Preheat your air fryer to 175°C (about 350°F). Grease a round 7-inch cake tin or similar-sized baking vessel that fits inside your air fryer basket. Pour the batter from Step 3 into the prepared tin, smoothing the top lightly. Place the tin in the air fryer basket and bake for 35-45 minutes, until a toothpick inserted into the center comes out clean or with just a few moist crumbs. The exact time depends on your air fryer's size and heat distribution.
Once baked, carefully remove the tin from the air fryer and let the cake cool in the tin for 10 minutes. This resting period allows the crumb structure to set slightly, making it easier to turn out without cracking. Turn the cake out onto a wire rack to cool completely before frosting or serving.