Combine graham cracker crumbs, brown sugar, 1/4 tsp salt and butter in a medium bowl. Spoon about 1 tbsp of the of the mixture onto the bottoms of 12 paper-lined muffin cups. Using the back of the measuring spoon, pack the crust down.
In another medium bowl, beat the cream cheese and sugar with a mixer until blended. Add the egg and vanilla and blend for about 30 more seconds. Spoon about 2 tbsp of the mixture into each muffin cup and level using the back of the measuring spoon.
Place into the oven and bake for 20 minutes. Let them cool completely. Refrigerate for 1 hour.
Place the caramels, milk, and 1/4 tsp salt in a small heat proof bowl. Place the boiling water into a pan. Place the bowl over the boiling water making sure it does not spill into the bowl. Let the caramels completely melt, stirring frequently.
Spoon about 1 tbsp of the caramel sauce over each cheesecake. Refrigerate for 1 hour. Sprinkle with remaining 1/4 tsp salt and serve.