In a small saucepan over medium heat, add the butter, cream, sea salt and vanilla and bring just barely to a boil. Reduce the heat to simmer, stir to dissolve the salt and hold at simmer to keep warm until needed.
In a 3 to 4 quart saucepan, add the corn syrup and sugar over medium heat. Allow the sugar to melt slowly, disturbing it as little as possible.
When you see liquid forming around the perimeter of the pan use a spatula to push the sugar toward the center and continue with this process breaking up any clumps. This will take a little patience and you will be tempted to stir and stir but resist the urge. If you stir it too much, the sugar will clump up before it has a chance to melt. If this happens turn the heat down very low and let it melt slowly without stirring.
As soon as the sugar is completely melted and the syrup is a nice amber color, remove it from the heat. It should smell like caramel at this point.
Slowly pour the hot cream mixture into the melted sugar whisking as you pour. Be very careful as there will be aggressive bubbling and it will appear that it will bubble over the pan. Keep stirring and it will settle down again. Continue to whisk the caramel to incorporate it well. Allow the sauce to cool for 10-15 minutes before pouring it into a container.
This sauce will appear thin until it cools down. Store it in the refrigerator for up to 3 weeks or in the freezer for 3 months. To serve, remove from the refrigerator and set the container into a dish or pan of hot tap water for 5 minutes and it will soften to a spoonable consistency.
Notes
It is helpful to use a long-handled whisk or wooden spoon when adding the cream mixture to the melted sugar as the bubbling action can splatter and the steam will burn.