In a medium bowl, add the flour, baking powder, and salt. Whisk together then set aside.
In the bowl of your stand mixer (or a large mixing bowl), add the butter and beat until creamy.
Slowly add in the sugar to the butter while the mixer is still running on low.
Add in the egg and vanilla and mix well. Scrape down the sides of the bowl and mix again until fully incorporated.
With the mixer back on low, slowly add in the flour mixture until just combined.
Remove the dough from the mixer and divide it into two equal chunks. The dough should be smooth and easy to work with, not sticky.
Put half of the dough back into your mixing b owl and add in the instant coffee. Mix until just distributed and the dough is speckled with coffee granules. Remove the coffee dough from the mixer.
Put the other half of the dough into the mixing bowl and add in the melted chocolate. Mix until well combined.
In between two sheets of wax paper, separately roll out each dough to an approximately 1/4" thick rectangle. Aim for an approximately 9" x 14" rectangle. Chill the rolled out dough, still in the wax paper, on baking sheets in the refrigerator for at least an hour (I left mine over night).
After the dough is thoroughly chilled, remove the wax paper and lay the chocolate dough on top of the coffee dough. Gently press the two doughs together using a rolling pin.
Let the dough stand at room temperature until easy to work with.
Use a knife to even out one side (the long side - ~14"). This will give you a smooth start for the spiral.
Tightly roll the dough, like a jelly roll, using your wax paper to guide the dough. Go slowly - the chocolate portion will likely tear. If that happens, pinch the dough back together then continue.
Cover the rolled dough in wax paper then in plastic wrap. Chill for at least an hour, turning the dough halfway through so it doesn't get flat on one side.
Preheat your oven to 350 degrees and line two baking sheets with parchment paper or silicone baking mats.
Remove the dough from the fridge, uncover and slice it in half using a sharp knife. Put half of the dough back in the fridge to keep it cold while you're working with the other half.
Cut the dough into 1/4" rounds.
Bake for 10-12 minutes. Remove from the oven and let cool on the sheets for 2-3 minutes before transferring to a cooling rack.