Preheat oven to 350 F. Spray a mini muffin tin with nonstick cooking spray.
Beat together butter and brown sugar until light and fluffy. Beat in vanilla and egg until well combined.
In another bowl, stir together flour, salt and baking soda. Add dry ingredients in 2 batches, mixing just until combined. Add oats and mix jus until oats are evenly incorporated.
Working with a heaping tablespoon of dough at a time, roll into balls and place in the holes of the muffin tin.
Bake until the edges of the cookie cups are firm and just beginning to brown (the centers should still look soft), 10 to 12 minutes. Let cookie cups cool completely in the muffin tin before removing. Trust me on this - they are very tender and may crumble if you remove them before they are cool. (Note: the centers of the cookie cups will sink as they cool. This provides the perfect spot for creamy frosting!)
When cookie cups are cool, make frosting by beating together cream cheese, powdered sugar, milk and vanilla extract until smooth. Add milk a bit more at a time, if needed to bring the mixture together, but you want it to be quite thick. Spoon frosting into a piping bag or Ziploc bag. Clip the end off and pipe frosting into each of the cookie cups.
If you'd like, top the cookie cups with caramel sauce and a sprinkling of oats just before serving.
Store the cookie cups in a sealed container at room temperature for up to 3 days. Fill and top just before serving.