Slice the carrots into 1½-inch-long pieces to ensure they cook evenly in the air fryer. For extra thick parts of the carrot, also slice them long ways to create two 1½-inch pieces. Place in a medium-sized bowl.
Melt butter in the microwave for 6-8 seconds. Add olive oil, honey, and brown sugar to the melted butter and stir well until combined.
Pour glaze over the sliced carrots and stir well to coat all sides of the carrots.
Preheat the air fryer for 2 minutes at 370ºF.
Add the coated carrots to the air fryer basket in a single layer. Carrots shrink as they cook, so it is okay to have slight overlaps in the basket.
Air fry for 8 minutes. Then, shake the basket to rearrange the carrots. Drizzle any remaining leftover glaze on top of the carrots. Continue to air fry for 4 minutes.
Test the tenderness of the thickest carrot with a fork. If needed, add 2 minutes to achieve more tenderness.
Place the air-fried carrots into a serving dish and sprinkle with fresh parsley.