Line an 8.5 x 4.5-inch loaf pan with parchment paper, leaving a 2-inch overhang on each side. Lightly butter the parchment; set aside.

Combine cream, corn syrup, sugar, and butter in a heavy-bottomed saucepan over medium-low heat. Stir until sugar dissolves. Clip a candy thermometer to the side. Bring to a boil.

Cook over medium heat, stirring frequently, until mixture reaches 246-248°F (120°C). Stir constantly as it gets close to temperature. Remove from heat, quickly stir in vanilla extract and salt. Immediately pour into prepared pan, without scraping the pot.

Let stand at room temperature until completely cooled and set, about 3-4 hours. Unmold using parchment overhangs. Peel off parchment and invert onto a clean surface.

Cut the slab into ½-inch thick strips, then into 1-inch pieces using a sharp knife or kitchen shears.

Sprinkle flaky sea salt over each caramel. Wrap individually in cellophane, parchment, or waxed paper soon after cutting to maintain shape.