In a large microwave-safe bowl, combine the butter, brown sugar, granulated sugar, corn syrup, cinnamon, and salt. Microwave on high for 1 minute, then stir until the mixture is smooth and melted.
Microwave the mixture for an additional 1-2 minutes, stirring every 30 seconds, until it turns a deep amber color and thickens slightly. Stir in the vanilla extract.
Pour the crisp rice cereal squares into a separate large mixing bowl. Drizzle the hot caramel mixture over the cereal, and gently toss with a silicone spatula until the cereal is evenly coated.
Sprinkle the powdered sugar over the caramel-coated cereal. Toss gently to coat the cereal completely, creating a light, powdery layer.
Add the finely chopped dried apples to the bowl and toss to distribute them evenly throughout the mixture. Let the mixture cool completely before serving.