In a medium mixing bowl, beat heavy cream on high until stiff peaks form, and then set aside.
In a large mixing bowl, beat the milk, peanut butter, and cocoa at medium speed until combined and smooth (it will be thick). Add the whipped cream, and beat at a low speed until combined. Then freeze for approximately 2 hours.
Heat your oven to 375° F and move your rack to the center of the oven. Then line a sheet pan with cooking parchment paper (approx 16×12 inches) and set aside.
In a small mixing bowl, combine flour, cocoa powder and baking powder, then set aside.
In a large mixing bowl, beat the eggs on high with your mixer until thick and lemon-colored (about 3 minutes). On low speed, gradually beat in the sugar, then add the water and vanilla and beat on low until combined. Add flour mixture gradually (in thirds) and beat on low, just until smooth. Pour the batter into your paper-lined pan, and spread to the corners.
Bake for 15 minutes or until a toothpick inserted in the middle comes out clean. Immediately remove paper with cake from the pan and set on a wire rack.
Place clean kitchen towel over the cake and begin to carefully roll the cake and towel (from the narrow end), pulling parchment off as you roll the cake and towel.
Cool the cake (rolled) on a wire rack 45 minutes to 1 hour. The cake must be cool before you go to the next step.
Once cooled, unroll the cake and remove the towel. Spread the ice cream over the cake, leaving ¼ of an inch border on all sides. Gently roll the cake back up, and freeze until firm.
Keep your cake in the freezer and slice to eat. Feel free to top as you like!