Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
Beat butter and sugar until light, about 2-3 minutes.
Add egg yolk, milk, and vanilla.
Stir in flour, cocoa powder, and salt until combined. Chill dough for 1 hour in the fridge.
Whisk egg white in a bowl until frothy. Prepare another shallow bowl with chopped pecans.
Divide dough into 20 evenly-sized pieces and roll into balls. Roll each ball in the frothy egg whites, then in the chopped pecans, pressing the nuts in to cover the cookie dough really well. Place on prepared baking sheet and press a finger or the back of a ½ teaspoon measuring spoon into the center of each ball to form an indentation.
Bake for 10-12 minutes, just until set. Be careful not to overbake.
While cookies are still hot, using the measuring spoon to press the indentation again so there is a good space for the caramel to go.
Combine the caramel and water in microwave-safe bowl and melt by heating in 20-30 second intervals and stirring in between, about 1-2 minutes total. Pour melted caramel into the depression in each cookie.
Melt semisweet chocolate with shortening in another microwave-safe bowl in 20 second intervals, stirring between each burst of heat, just until melted, about 1-2 minutes.
Transfer the melted chocolate to a ziplock bag and make a small snip off one corner. Drizzle the chocolate over the cookies, then let set before serving.