Line an 8-inch square baking 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 * 4 1/2 inches deep), stir together 1/4 cup water with the sugar, and corn syrup, and bring to a boil over medium-high heat. Continue to boil until the mixture 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, in a small pan, bring the cream, butter, and 1 teaspoon of fleur de sel to a simmer over medium heat. Turn off the heat, and set aside.
When the sugar mixture is a warm golden color, turn off the heat and slowly add the cream mixture to the sugar mixture. Be careful! It will bubble up violently. Stir in the vanilla with a wooden spoon and cook over medium low heat for about 10 minutes, until the mixture reaches 248 degrees (firm ball) on a candy thermometer. Very carefully (it's hot!) pour the caramel into the prepared pan and refrigerate for a few hours until firm.
When the caramels are cold, pry the sheet from the pan onto a cutting board. Cut the sheet in half. Starting with the long end, roll the caramel up tightly into an 8 inch log. Repeat with the second piece. Sprinkle both logs with fleur de sel, trim the ends, and cut each log in 8 pieces. Cut glacene or parchment papers into squares and wrap each caramel in a paper, twisting the ends. Store in the refrigerator and serve the caramels chilled.