Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
In a food processor, combine both sugars and the marzipan. Process until they resemble a fine sand, about 1 minute
Transfer mixture to a large bowl. Add the butter, vanilla, baking powder, baking soda, salt and egg.
Use an electric mixter to beat until smooth, scraping down the bowl once during mixing, about 2 minute.
Add flour and cocoa powder and mix until incorporated, scraping down the bowl once dufing mixing, about 1 minute The dough should be very stiff.
Baking in batches, drop 1 T. balls of dough on the prepared baking sheet, leaving about 2 inches around all sides. Bake on the oven's lower rack until cookies are flat and have a crackled surface, about 10 minute.
The cookies will be very soft. Let them cool for 5 minute on the baking sheet, then transfer to a rack to cook completely. If desired, once the cookies are cool, dust them with powdered sugar.