Separate egg; set egg yolk aside. Cover and chill egg white until needed. Stir together flour, cocoa powder, and salt; set aside.
In large bowl, beat butter with electric mixer on medium to high speed for 30 seconds. Add sugar; beat until combined. Beat in egg yolk, milk, and vanilla. Beat in as much of the flour mixture as you can with mixer. Stir in any remaining flour mixture. Cover and chill about 2 hours or until dough is easy to handle.
Preheat oven to 350°F In small saucepan, cook and stir caramels and whipping cream over low heat until mixture is smooth. Set aside.
Slightly beat reserved egg white. Shape dough into 1 inch balls. Roll balls in egg white, then in pecans to coat. Place balls 1 inch apart on greased cookie sheet. Using your thumb, make indention in center of each cookie.
Bake about 10 minutes or until edges are firm. Spoon melted caramel mixture into indentation. (If necessary, reheat caramel mixture to keep it spoon able.) Transfer cookies to wire rack; cool.
In another small saucepan, combine chocolate chips and shortening. Cook and stir over low heat until melted. Cool slightly. Drizzle cookies with chocolate mixture. Let stand until chocolate is set.