Line a loaf pan (8.5 x 4.5 inch) with parchment paper, leaving overhang on the long sides for easy removal.
In a small saucepan over medium-low heat, melt the butter. Add the brown sugar erythritol and heavy whipping cream. Stir continuously for 3 to 4 minutes until the mixture is smooth, bubbling gently, and slightly thickened. Remove from heat and stir in the vanilla extract, caramel extract, and sea salt.
In a mixing bowl, beat the softened cream cheese with an electric mixer until completely smooth and free of lumps, about 2 minutes. Slowly pour the warm caramel mixture into the cream cheese while beating on low speed. Increase to medium speed and beat for 1 minute until silky.
Pour the fudge into the prepared pan and smooth the top with a spatula. Sprinkle flaky sea salt generously over the surface.
Freeze for 2 hours until completely firm. Lift the fudge out using the parchment overhang, let sit at room temperature for 5 minutes, then cut into small squares with a sharp edge. Store in the refrigerator.
