Soak gelatin in cold water.
Heat milk with vanilla until just simmering.
Whisk yolks with sugar; stir in dissolved gelatin.
Return to saucepan; cook over medium heat to 83 °C, stirring constantly.
Strain over chopped white chocolate; let sit 1 minute, then stir until melted.
Cool to ~30 °C, stirring occasionally.
Whip cream to soft peaks; fold into the chocolate mixture.
Fill the silicone mold with mousse, ensuring all ridges are filled.
Unmold the frozen caramel–coffee–crunch insert; press into mousse so edges align.
Freeze overnight.