Spray a half-pan baking sheet with vegetable-oil spray; line with parchment paper and spray the parchment. Set aside.
Put cream, corn syrup, sugar and butter in a large stockpot. Bring to a boil over high heat,stirring to melt butter and dissolve sugar, about 10 minutes. Cook over medium-high heat,stirring often, until temperature reaches 248 degrees F (firm-ball stage) on a candy thermometer, about 20 minutes.
Remove from the heat and stir in vanilla and medium grind sea salt until combined. Immediately pour into the prepared pan without scraping the pot. Sprinkle coarse-grind sea salt in an even layer over the top. Let stand, uncovered, at room temperature for 24 hours without moving.
Using a large knife, cut around outside of caramel in pan. Lift caramel out of pan and remove parchment paper. Cut into 1 by 1 1/4 inch pieces or other shapes. Wrap each piece in cellophane or waxed paper so they can keep their shape.