Line the bottom of an 8-inch square baking pan (or loaf pan) with parchment paper, then brush the paper lightly with oil, allowing the paper to drape over 2 sides.
In a deep saucepan (6 inches diameter by 4 1/2 inches deep) combine the sugar, corn syrup, and 1/2 cup water and bring to a boil over medium-high heat. Continue to boil until the caramel is a warm golden brown color. Don't stir - just swirl the pan to mix. Watch carefully, as it will burn quickly at the end!
In the meantime, bring the cream, butter, and 1 teaspoon fleur de sel to a simmer in a small pan over medium heat. Remove from the heat, set aside and keep warm.
When the caramelized sugar is the right color, slowly add the cream mixture to the caramel - it will boil up violently. Stir in the vanilla with a wooden spoon and cook over medium heat for 5 to 10 minutes, until the mixture reaches 248 degrees F (firm ball) on a candy thermometer. Very carefully (it's hot!) pour the caramel into the prepared pan and refrigerate until firm.
When the caramels are cool, use the parchment paper to pry the sheet from the pan onto a cutting board. Starting at 1 end, roll the caramel up tightly until you've rolled up half of the sheet. Cut the sheet across and then roll the second half tightly. You will have 2 (1 by 8-inch) logs. Sprinkle both logs lightly with fleur de sel, cut each log in 8 pieces. Cut parchment papers in 6 by 4 1/2-inch squares and wrap each caramel in a paper, twisting the ends. Store in the refrigerator or at room temperature.