Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the graham cracker crumbs, flour, Dutch-process cocoa powder, baking powder, baking soda, and kosher salt.
In the bowl of a stand mixer fitted with the paddle attachment, or using a hand mixer, beat the softened butter and dark brown sugar together until light and fluffy, about 2–3 minutes.
Scrape down the bowl and add the eggs one at a time, mixing well after each addition. Add the vanilla extract and heavy cream and mix just until incorporated.
Add the dry ingredients to the wet ingredients. Mix on low speed just until the batter comes together and no dry streaks remain. Do not overmix.
Let the batter rest at room temperature for about 20 minutes. This allows the batter to firm up slightly, which helps the cakes hold their shape better while baking.
Using a medium cookie scoop, scoop the batter onto the prepared baking sheets, leaving at least 2 inches between each portion. Gently smooth the tops if needed.
Bake for 10–12 minutes, or until the cakes are set and spring back lightly when gently pressed in the center. Do not overbake.
Allow the cakes to cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.