Prepare a 9×13-inch pan by spraying it with nonstick cooking spray.
In a large pot, melt the 1/4 cup butter over medium heat. Add the mini marshmallows and stir until just melted. Remove from heat.
Add the Cheerios™ cereal and freeze-dried strawberries to the melted marshmallow mixture. Stir until everything is evenly coated.
Press the mixture into the prepared pan, spreading it out evenly. Allow it to cool completely before cutting into 16 bars.
In a microwave-safe bowl, melt the white chocolate chips and 2 tablespoons of butter or coconut oil in 30-second intervals, stirring between each, until smooth.
Dip the bottom of each cereal bar into the melted chocolate and place on a sheet of parchment paper with the chocolate side up. Allow the bars to cool and the chocolate to set before serving.