In a microwave-safe bowl or using a double boiler, melt the white chocolate with the butter. If using a microwave, heat in 30-second bursts, stirring between each until fully melted and silky smooth. Set aside.
In a separate medium saucepan over low heat, add the mini marshmallows. Stir constantly with a heat-resistant spatula until the marshmallows are completely melted with no lumps remaining. Once smooth, pour in the melted white chocolate mixture and stir until fully combined.
Place the popped popcorn in a large mixing bowl and pour the warm marshmallow-chocolate mixture over the popcorn. Add a few drops of blue food color. Then, using a rubber spatula, gently fold everything together, making sure the popcorn is evenly coated. The food color will create fun streaks of blue as you mix.
Sprinkle the red sprinkles over the coated popcorn while it's still sticky, then transfer the mixture to a parchment-lined baking sheet. Spread it out into an even layer, separating any large clusters. Allow the popcorn to sit at room temperature for about 30 minutes, or until the coating has fully set and hardened.