Add the butter, sugar, cocoa, and sea salt to the bowl of food processor. Pulse a few times to combine, then scrape down the sides of the bowl. Process for 30 seconds until mixture is smooth.

Add the corn syrup and vanilla and process 10 seconds to combine. Add the cooled melted chocolate and pulse a few times. Scrape down the sides of the bowl, then process 10 seconds until mixture is creamy.

Use the frosting within 3 hours. If making in advance, transfer the frosting to an airtight container and refrigerate for up to three days. Bring to room temperature for at least an hour before using.

Refrigerate leftover frosted cake.