Preheat oven to 350°F Line a baking sheet iwth parchment paper.
In a food processor, combine both sugars and marzipan. Process until they resemble a fine sand, about 1 minute. Transfer mixture to a large bowl. Add butter, vanilla, baking powder, baking soda, salt and egg.
Use an electric mixer to beat until smooth, scraping down the bowl, once during mixing, about 2 minutes.
Add flour and cocoa powder and mix until incorporated, scraping down once during mixing, about 1 minute. The dough should be very stiff. Baking in batches, drop 1 tablespoons balls of dough on prepared 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 minutes.
The cookies will be very soft. Let them cool for 5 minutes on the baking sheet, then transfer to a rack to cool completely. If desired, once cookies are cool, dust them with powdered sugar.