From TikTok's on_est_gourmands
Place an 8-inch skillet over medium heat and generously grease it with some butter. Once the skillet is hot, pour 3–4 Tablespoons (closer to 3 is best) of batter into the center of the pan. Tilt/twirl the pan so the batter stretches as far as it will go. The thinner the crepe, the better the texture.
Cook for 1–2 minutes, then flip as soon as the bottom is set. Don’t wait too long to flip crepes or else they will taste rubbery. Cook the other side for 30 seconds until set. Transfer the cooked crepe to a large plate and repeat with the remaining batter, making sure to butter the pan between each crepe. If desired, separate each crepe with parchment paper so they do not stick together. If you’re using enough butter in your pan, though, the crepes shouldn’t stick.
Top off with a sprinkling of cocoa powder. Chill.
I think lightly chilling the cake between layers will help keep the cremes a bit more solid, so they will not smush when a new layer is added.