For the ganache
Place chocolate in a medium-sized heat-proof bowl. Set aside.
In a small saucepan, heat cream over medium-low heat until steaming. Remove from heat and pour evenly over chocolate. Cover bowl with foil and let sit for 5 minutes.
After 5 minutes, whisk chocolate and cream mixture until smooth. Let sit until solidified (you can speed this up by placing the bowl in the refrigerator). Meanwhile, begin preparing cookie dough.
For the cookie dough
In a large mixing bowl, combine butter and sugar and beat with an electric mixer until light and fluffy.
Add egg, egg yolk, and vanilla extract. Stir until well combined.
In a separate medium-sized mixing bowl, whisk together cake flour, dark cocoa powder, cornstarch, baking powder, baking soda, and salt.
Gradually add the dry mixture to the wet ingredients, stirring until completely combined. Cover dough with plastic wrap and chill in the refrigerator for 30 minutes.
Form ganache into balls
Once ganache has solidified, scoop into Tablespoon sized portions and drop onto a wax paper lined cookie sheet and place in the freezer.
Assembly
When cookie dough is nearly done chilling, preheat oven to 375F (190C) and line baking sheets with parchment paper. Set aside.
Scoop ¼ cup of cookie dough and roll gently between your palms to create a smooth ball. Using your thumbs, press a crater just into the center of the dough (don’t press too deep, or the filling will spill out the bottom of the cookies after baking). Retrieve one dollop of ganache from the freezer, press into the crater, fold dough over ganache so there is no ganache showing. Roll gently between your palms to create a smooth ball, make sure all of the ganache is covered. Repeat with remaining dough and ganache.
Place on prepared cookie sheet, spacing cookies at least 2” apart. Transfer to center rack of 375F (190C) oven and bake for 13 minutes.
(Optional) Within one minute of coming out of the oven, take a large flat bottomed measuring cup and gently flatten the tops of the cookies for a lava cake appearance. Do not press too hard or the ganache will leak!
Let cookies cool on the cookie tray, then sift powdered sugar over the tops before serving. Enjoy!