Heat milk, cream, sugar, and espresso powder in a saucepan until warm (but not boiling).
In a separate bowl, whisk egg yolks until smooth.
Slowly pour warm milk into yolks, whisking constantly to avoid scrambled eggs.
Return mixture to the stove, stirring over low heat until it thickens slightly.
Strain the custard, then let it cool completely before refrigerating for at least 2 hours.
While chilling, make caramel by melting sugar in a pan until golden.
Stir in butter and heavy cream, whisking until smooth.
Add sea salt, remove from heat, and let it cool.
Churn the ice cream base in an ice cream maker according to instructions.
Once thickened, swirl in caramel sauce before transferring to a container.
Freeze for at least 2 more hours to firm up.
Scoop, enjoy, and pretend you’re sharing.