Melt the white chocolate in short bursts in the microwave or over a double boiler, stirring often since it burns easily. Let it cool for a few minutes.
Add the ice cream, milk, melted white chocolate, vanilla extract, and salt to a blender.
Blend on high for 20–30 seconds until smooth and creamy, scraping down the sides if needed.
Taste and adjust — add more milk for a thinner shake or more melted chocolate for extra sweetness.
Pour into a chilled glass, top with whipped cream and white chocolate shavings, and serve immediately.