While your chocolate cups set in the fridge, begin to make your caramel oat filling.
Add sweetened condensed milk, brown sugar, butter, and salt to a pan and bring to medium-low heat, stirring and scraping the edges of the pot continuously to avoid burning the sugar. Once the mixture starts to bubble slightly, bring heat to low.
Continue to stir, with heat on low for a total of around 8 minutes. The consistency of your caramel mixture should start thickening, and will continue to thicken once it starts to cool. You can check the consistency by submerging a small spoonful of caramel in a bowl of ice water—this will essentially speed up the cooling process and give you an idea of how your caramel is coming along! Be sure you don't leave your caramel unattended though—caramel has a tendency to burn very easily! Remove caramel from the heat and mix in vanilla extract, then mix in oats.
Give your caramel filling a maximum of a minute or two to cool slightly before pulling your chocolate cups out of the fridge.
Fill up each cup with the caramel oat filling, gently pressing down with your fingers or the back of your spoon to flatten out the top of the filling.
Place your cups back in the fridge to allow the chocolate to re-harden and the filling to cool down completely.