In a medium pot over medium heat, whisk together sugar, light syrup, and milk. Stir constantly until the mixture just begins to boil. Remove from heat and pour over butter.
In a separate medium bowl, whisk together flour, baking powder, salt, and gingerbread spice.
Once butter mixture is lukewarm, add dry mixture, stirring to combine. Form dough into a ball or blob, then wrap in cling film. Refrigerate for 1–2 hours or (ideally) overnight.
After your dough has chilled, line a few baking sheets with parchment paper.
Retrieve one-sixth to one-fourth of dough from fridge. (Leave the remaining dough in fridge to keep it cool.)
Take about 2 teaspoons (10g) of dough and roll into a fat log that’s slightly tapered at one end. Place on lined baking sheet with tapered end facing you.
With lightly floured hands, flatten dough log with your fingers into a pinecone shape that’s 1/8-inch (3mm) thick. Repeat with the rest of your current dough blob. NOTE: If at any point your dough starts to get too warm and sticky, put it back in the fridge to chill again.
Next you will make the pinecone design with a symmetrical paring knife. You will hold the knife flat and parallel to the dough before pressing the tip straight down into the dough to create wee triangles. Starting at the fatter end of the pinecone (the end farther away from you), make 3 triangle impressions directly next to each other. Move down to the next line and make triangle impressions in between the first row of triangles. Continue this staggered pattern down the entire pinecone.
Repeat and create pinecone design on remaining cookies.
Place baking sheet in fridge to chill for 20–30 minutes.
While pinecones are chilling, heat oven to 350°F.
Bake for 10 minutes until edges have set and cookies are golden.
Allow cookies to cool for 10 minutes on baking sheet, then transfer cookies to a wire rack to cool completely.
Once your cookies are totally cool, pour some cocoa powder into a small bowl. With a clean, small, food-only brush, use a light touch to brush cocoa powder from top of pinecone (narrower end) to the bottom (fatter end). The cocoa powder will gather in the knife impressions, and you’ll see the pinecone pattern appear before your very eyes.
Repeat with remaining dough until you’ve created all your pinecones. 
We recommend a dark cocoa powder, such as Valrhona or King Arthur Baking black cocoa. We found that Hershey’s wasn’t dark enough to really show off the pinecone-iness.
Obviously overlapping some of the steps for different batches will be the most time efficient. But to keep these directions simple, we’ll let you sort out the method that works best for you!