Mix semisweet chocolate chips and white chocolate chips together in a large bowl.

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Bring cream to a boil in a small saucepan; remove from heat and pour over chip mixture. Stir mixture until chips are melted. Beat confectioners’ sugar into chocolate mixture using an electric mixer until smooth and thin. Refrigerate until completely cooled and thickened, at least 30 minutes. Beat mixture again with an electric mixer until frosting is fluffy and light brown.