In a medium saucepan, heat the sugar over medium heat, stirring until it melts into a golden amber liquid, about 8-10 minutes. Add the butter and whisk until melted, then pour in the heavy cream while stirring. Remove from heat, add flaky sea salt, and set aside to cool.

In a mixing bowl, whisk together the egg yolks and granulated sugar until creamy and pale, about 2-3 minutes. Heat the whole milk and heavy cream in a saucepan over medium heat until it simmers. Gradually add the hot milk mixture to the egg yolks, whisking constantly, then return to the saucepan and cook over low heat until thickened.

Strain the thickened custard through a fine-mesh sieve into a clean bowl to remove any cooked egg bits. Cover with cling film and refrigerate for at least 4 hours or overnight until completely chilled.

Pour the chilled custard into the ice cream maker and churn according to manufacturer’s instructions, about 20-25 minutes. Drizzle in the cooled salted caramel sauce during the last few minutes of churning.

Transfer the ice cream to an airtight container. Smooth the top, cover with cling film, and freeze for at least 4 hours or overnight to firm up before serving.