Line an 8-inch square baking pan with aluminum foil, leaving enough overhang on the sides for easy removal later. Lightly coat the foil with butter to prevent sticking.
In a sturdy 3-quart saucepan, combine the heavy cream, granulated sugar, brown sugar, and corn syrup. Set the pan over medium heat and stir continuously with a wooden spoon until the sugars dissolve and the mixture becomes thick and slightly opaque.
Once the mixture begins to boil, use a pastry brush dipped in water to gently wash down the sides of the pan, preventing sugar crystals from forming. Secure a candy thermometer to the pan, ensuring it doesn’t touch the bottom to get an accurate reading.
Allow the caramel to cook undisturbed until it reaches 245°F (118°C). As soon as it reaches the target temperature, remove the pan from heat immediately. Carefully stir in the salt, vanilla extract, vanilla bean seeds, and softened butter. Be mindful as the mixture may bubble vigorously.
Pour the hot caramel into the prepared pan, spreading it evenly. If desired, sprinkle a light dusting of coarse sea salt over the top for an extra touch of flavor. Let the caramel cool completely at room temperature, uncovered, for at least 4 hours or overnight.
Once fully set, lift the caramel slab from the pan using the overhanging foil. Gently peel away the foil and transfer the caramel to a cutting board. With a sharp knife, cut into uniform squares or rectangles. If preferred, wrap each piece in candy wrappers for easy storage and gifting.