Preheat oven to 350 degrees F. Line 1 muffin tin with paper liners. Set aside.
In a medium bowl, combine the graham cracker crumbs, brown sugar, and melted butter and stir until moistened and mixture resembles wet sand. Using a Tablespoon measuring spoon, spoon about a Tablespoon or so of the mixture evenly among the muffin cups. Use the bottom of a spice jar to compress the graham cracker mixture neatly into the bottom of each muffin cavity. Bake for 5 minutes. Remove from oven but keep oven on.
Meanwhile, in the bowl of a stand mixer, cream together the cream cheese and brown sugar with the paddle attachment until smooth and creamy, about 1 minute. Scrape down the sides of the bowl and add in the eggs, one at a time, beating well after each addition. Add in the vanilla and sour cream, beating well and scraping down sides if necessary, followed by the salted caramel sauce. Mixture should be very smooth.
Using a cookie dough scoop, scoop about 2 Tablespoons of cheesecake among each muffin cup, filling about 3/4 of the muffin cavity. Bake for 15-17 minutes or until cheesecake tops are very light golden brown and the centers appear set and not jiggly. Cool completely.
Once cooled, spoon a Tablespoon of salted caramel on top of each cheesecake and then refrigerate to set, about 1 hour.