Preheat oven to preheat to 350°F (180°C). Spray a muffin pan with nonstick spray or line with cupcake liners and set aside.
Make the brownie cups: Whisk the melted butter, oil, and sugars together until well combined, about 1 minute. Add the eggs and vanilla; beat until lighter in color, about 4 minutes.
Sift in the flour, cocoa powder, and salt. Gently fold the dry ingredients into the wet ingredients with a rubber spatula until just combined.
Equally spoon the batter into the prepared muffin pan and bake for 15-20 minutes. If testing with a toothpick, the toothpick should come out with a few wet crumbs (not batter) for fudge-textured brownies.
Make the salted caramel: Heat the granulated sugar in a medium saucepan over medium heat, stirring constantly with a high heat resistant rubber spatula or wooden spoon. Sugar will form clumps and eventually melt into a thick brown, amber-colored liquid as you continue to stir. Be careful not to burn.
Once sugar is completely melted, immediately add the butter and stir until melted and combined, about two minutes. (Be careful with this step because the caramel will bubble rapidly when the butter is added.)
Very slowly drizzle in the heavy cream while stirring. Allow the mixture to boil for 1 minute then remove from heat and stir in the salt. Allow to cool down before using it. (Caramel thickens as it cools.)
Once your brownies have finished cooking, remove the pan from the oven and allow them to cool and set in the pan. Sprinkle some flaky sea salt on top of brownies immediately after removing them from the oven
Drizzle some caramel sauce on top of the cooled brownies & enjoy!
Allow brownie cups to cool completely in the pan, otherwise, they'll be difficult to remove in one piece! Alternatively, you can bake these in cupcake liners, just be sure to spray the liner with nonstick cooking spray.