Beat the butter for 3-5 minutes until creamed - look for it to be light and fluffy. Add both sugars and beat one minute more. Make sure to scrape down the sides to make sure everything's combining evenly.
Add egg yolk and vanilla extract and beat until combined.
Add the flour in 3 batches, mixing on low until just incorporated. In the middle of adding flour, sprinkle in salt.
Use your hands to roll 1 inch balls, then use a knuckle to make an indent in the middle. Chill for several hours, ideally overnight.
Preheat the oven to 375°F and place cookies on an ungreased cookie sheet. They won't spread too much, so you don't have to worry about spacing more than an inch or two apart.
Bake 10-12 minutes. When the bottom edges are just beginning to darken, they're done. If necessary, use a teaspoon measuring spoon to re-shape the thumbprint as soon as you take them out from the oven.
Let cookies cool completely before filling. Make caramel while they cool (recipe link above).
Using a small spoon or teaspoon, spoon warm caramel into cookies. Let cool fully before serving.