Place the cookies in a large bowl and roughly crush them with your hands. Set aside.
Separate the eggs, reserving only the egg yolks for this recipe.
Melt the butter over low heat and set aside.
Place the dark and milk chocolate in a saucepan.
Add the egg yolks, sugar, heavy cream, vanilla extract, and melted butter.
Whisk the mixture continuously over medium heat until the chocolate melts and the ingredients are well combined, forming a smooth, glossy chocolate sauce. Bring to a gentle simmer, then remove from the heat and set aside.
Pour the chocolate sauce over the crushed cookies and stir until everything is evenly combined.
Lightly grease a large ring cake pan and transfer the mixture to it. Alternatively, line a large loaf pan with parchment paper, pressing it into the bottom and up the long sides, with an equal amount of overhang on each side, as shown in the video. Transfer the mixture to the prepared pan and press it down evenly.
Freeze overnight, preferably for 24 hours, until completely firm.
Remove the Lazy Cake from the pan and place it on a serving plate. If using parchment paper, gently peel it away.
Serve the Lazy Cake frozen, just as you would an ice cream cake. Cut off the desired number of slices, wrap the remaining cake tightly in plastic wrap, and return it to the freezer.