Prep the baking dish: Line an 8×8 baking dish with parchment paper, leaving enough overhang on two sides to lift the cooled caramel out easily. Grease the parchment with butter.
Combine the sugars and syrup: In a large heavy-bottomed dutch oven, add the granulated sugar, brown sugar, and corn syrup. Stir gently to combine, then heat over medium until the mixture begins to melt and bubble. Avoid stirring too much, as it can cause crystallization.
Add the butter: Once the mixture reaches a steady boil, add the butter cubes and stir until fully melted and smooth.
Pour in the cream: Slowly stream in the heavy cream. The mixture will bubble vigorously, so pour carefully. Continue stirring until everything is smooth again.
Cook to temperature: Attach a candy thermometer and let the caramel cook until it reaches 238–242°F (soft-ball stage). Stir occasionally to prevent scorching.
Finish with flavor: Remove from heat and stir in the vanilla extract and fine sea salt. Mix until glossy and well combined.
Cool and set: Carefully pour the hot caramel into your prepared baking dish. Allow it to sit for about 10 minutes, then sprinkle with flaky sea salt once the surface has thickened slightly.
Chill and cut: Let the caramel cool completely in the fridge or at room temperature. Once fully set, lift the slab out using the parchment flaps and transfer it to a cutting board. Cut into 1" × ⅔" rectangles using a sharp, non-serrated knife or a bench scraper. Wrap each caramel in a 4" × 5" wax paper square.