Crush the cookies into fine crumbs, then mix with the melted butter. Press the mixture into the bottom of a springform pan and refrigerate for 30 minutes.
Melt the white chocolate over a double boiler, then let it cool slightly.
Soak the gelatin sheets in cold water for 5 minutes, then heat over low heat until completely dissolved.
Whip the heavy cream until stiff peaks form. Add the sugar and vanilla extract, then slowly incorporate the melted white chocolate and dissolved gelatin.
Divide the mousse mixture into six equal portions. Add a different food coloring to each portion (red, orange, yellow, green, blue, purple).
Layer the colored mousse layers into the springform pan, starting with red and progressing towards purple. Smooth each layer gently.
Refrigerate the cake for at least 6 hours to allow it to set and the layers to stabilize.
Before serving, decorate with rainbow-colored sprinkles or white chocolate shavings.
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