Prepare a baking sheet or a marble or granite slab by spreading some butter in a 15"x15" area. (The caramel will probably spread to about 12" or 13", but having extra is good.
Put the cream, sugar and corn syrup into a small saucepan over medium heat.
Cook, stirring continuously until mixture reaches 250°F on a candy thermometer. Mixture will boil, modulate the heat on your stove so it doesn't boil over.
When mixture reaches 250°F, remove the pan from the heat and stir in the vanilla and ¼ teaspoon table salt. Mixture will sizzle a little, but stir until combined.
Then immediately pour the caramel onto the prepared surface.
Sprinkle the sea salt over the top of the caramel and let cool, at least 2 hours.
When mixture is completely cooled start at the long edge, if there is one, mine spread into an almost a perfect circle, and roll up tightly.
Butter the edge of a bench scraper or knife and cut 36 pieces.
Wrap each piece in waxed paper.