Preheat the oven to 300°F (150°C). Line a baking sheet and arrange the dinner rolls spaced slightly apart; cover the rolls loosely with aluminum foil.
Bake the covered rolls for about 15 minutes, or until they are lightly browned and warmed through, then remove the foil.
In a small microwave-safe bowl, melt the butter in 10-second intervals until fully liquid. Stir in the honey and brown sugar until the mixture is smooth.
Brush the tops of the hot rolls evenly with the honey-butter mixture using a silicone brush.
Preheat the air fryer to 390°F (200°C). Place the chicken bites in a single layer in the basket—do not overcrowd—and cook for about 5 minutes or until heated through and crispy.
Return the rolls to the oven, uncovered, for 5 minutes to set the glaze and finish warming; then remove and let the rolls cool for 3–5 minutes so they are easy to handle.
Using a butter knife, slice each roll horizontally about halfway through. Place one chicken bite inside each roll.
Optional: Drizzle additional honey over the assembled chicken minis if desired, then serve warm.