Preheat the oven to 350°F and prepare the mini cupcake pan with non-stick spray.
Place the graham crackers in a plastic bag and smash with a rolling pin or something heavy (you can use a food processor to do this, just make sure you don't pulverize the crackers into dust). Put the graham cracker crumbs, flour, baking soda, and salt in a small mixing bowl and mix together completely.
Place the butter and both sugars in a large mixing bowl and cream together with a hand mixer for 2-3 minutes (you can also do this in your stand mixer). Add the egg and vanilla and fully combine.
Pour the dry ingredients in with the butter mixture and blend together at low speed until combined. The mixture will be very crumbly at this point, that is what you want.
Scoop out about a tablespoon of dough and roll it into a ball. Place the ball into the mini cupcake pan and press down lightly to pack it in. Bake for 8 minutes. Remove the pan from the oven and place it onto a cooling rack.
Immediately after baking, take a rounded spoon (my measuring spoon worked great) and make a small well in each of the warm cookie cups.
Place a chocolate kiss in the middle of each cup and allow the cups to cool. The chocolate will become soft from the heat.