For this recipe, you will need an accurate candy thermometer. You'll also need to cut three-inch square pieces of waxed paper or cellophane in which to wrap the caramels.
Lightly brush bottom and sides of a 9-by-13-inch rimmed baking sheet with oil. Line with parchment, leaving a 2-inch overhang on long sides; lightly brush parchment with oil. Sprinkle 1/3 cup sesame seeds on parchment-lined baking sheet.
Bring cream, sugar, butter, and corn syrup to a boil in a large saucepan over high heat, stirring until sugar dissolves. Reduce heat to medium-high; cook, stirring occasionally, until caramel reaches 248 degrees on a candy thermometer, about 15 minutes.
Immediately remove caramel from heat, and stir in salt, vanilla, and ginger. Pour caramel onto baking sheet, sprinkle with remaining 1/3 cup sesame seeds, and let stand, uncovered, at room temperature at least 8 hours and up to 1 day.
Lifting by parchment overhang, transfer caramel to a large cutting board. Cut into 3/4-by-1 1/4-inch pieces; wrap each piece in waxed paper or cellophane.