Preheat the oven to 350°F (180°C). Grease a 9-inch (23cm) round cake pan with cooking spray and line the bottom with parchment paper.
In a medium bowl, sift together the flour, cocoa powder, and baking powder.
In a liquid measuring cup, whisk together the boiling water and instant coffee.
To the bowl of a stand mixer fitted with the whisk, add the eggs, egg yolk, sugar, sesame oil, vanilla, and salt. Beat on medium-high speed until thickened and lightened in color, about 2 minutes. Beat in the sesame paste.
With the mixer on lowest speed, add half of the flour mixture and (immediately) half of the coffee mixture. Mix until just combined. Repeat, mixing until just combined. Scrape the batter into the prepared cake pan.
Bake until the top is dry and a toothpick inserted into the center of the cake comes out mostly clean with a few sticky crumbs, 32 to 34 minutes.
Transfer the pan to a wire rack and let cool for 10 minutes. Run a small offset spatula around the perimeter to loosen the edges. Invert the cake onto the wire rack. Remove the parchment. Invert again onto another wire rack so it sits right side up. Let cool completely before transferring to a cake plate.