Line an 8×8-inch pan with parchment paper and lightly grease.
Heat sugar in a heavy saucepan over medium heat until melted and amber in color.
Carefully add butter and stir until fully melted.
Slowly pour in warm cream, stirring constantly until smooth.
Cook the mixture until it reaches 245°F (firm-ball stage) on a candy thermometer.
Remove from heat and stir in vanilla and fine sea salt.
Pour caramel into the prepared pan and smooth the top.
Sprinkle with flaky sea salt and let cool completely.
Cut into squares and wrap individually.