Preheat oven to 375 degrees, with racks in upper and lower thirds. In a large bowl, beat together butter and sugar with a wooden spoon or electric mixer until pale and fluffy; stir in egg yolk.
In another bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt; stir flour mixture into butter mixture until a dough forms. Drop dough by level teaspoons, 1 inch apart, onto two parchment-lined baking sheets.
Bake until cookies are puffed and cracked, about 8 minutes, rotating sheets halfway through. Remove sheets from oven and tap firmly on a counter to flatten cookies. Transfer cookies to wire racks and let cool completely. (To store, keep in an airtight container, up to 3 days.)
Make frosting: In a bowl, beat together caramel and butter with a wooden spoon until smooth; gradually beat in confectioners sugar until smooth. Spread frosting on flat sides of half the cookies and top with remaining cookies.
The caramel frosting can also be used for a chocolate layer cake.