Prepare the Cookies:
With electric mixer on medium-high speed, beat butter and sugar until light and fluffy, about 2 minutes. Add egg yolk, milk, and vanilla; mix until incorporated. Reduce speed to low and add flour mixture until just combined.
Whisk egg whites in a bowl until frothy. Place chopped pecans in another bowl. Roll chilled dough into 1-inch balls, dip in egg whites, and then roll in pecans. Place balls about 2 inches apart on a baking sheet. Using a 1/2 teaspoon measuring spoon, make an indentation in the center of each dough ball.
Prepare the Caramel Filling:
Once cookies are removed from the oven, gently re-press the indentations. Fill each indentation with about 1/2 teaspoon of the caramel mixture. Cool on the pan for 10 minutes, then transfer to a wire rack to cool completely.
Prepare the Chocolate Drizzle (optional):
Place chocolate and shortening in a small zip-top plastic bag. Set bag in a bowl of warm water to soften. Gently knead the chocolate with your fingers until melted and smooth, placing back in the warm water for a minute or two as needed.