Preheat oven to 350°F (175°C). Line a jelly roll pan with parchment and grease lightly.
Whisk flour, cocoa, baking powder, and salt in a bowl.
Beat eggs and sugar for 3 minutes until thick and pale. Add vanilla.
Fold in dry ingredients, alternating with milk and melted butter. Don’t overmix.
Pour into pan, spread evenly, and bake 12–15 minutes until a toothpick comes out clean.
Turn cake onto a sugar-dusted towel, peel off parchment, and roll up gently. Cool completely.
Beat cream, caramel sauce, powdered sugar, and vanilla until soft peaks form. Chill if needed.
Heat cream, pour over chocolate and butter, let sit, then whisk smooth.
Unroll, spread caramel cream, and re-roll without the towel.
Drizzle with ganache. Let set, then slice and serve.