Heat oven to 375f.
Grease a 15x10x1 baking or jelly roll pan.
Line it with a waxed paper rectangle cut 1/2 inch smaller than the pan (14x9).
Grease the paper.
Sift flour, cocoa, baking powder and salt into a bowl or onto another sheet of waxed paper.
Beat eggs until thick and creamy.
Beat in sugar, 1 tbsp a time until mixture is thick.
Stir in water and vanilla.
Fold in flour mixture.
Spread batter evenly into prepared pan.
Bake 12-15 minutes until center spring back when pressed lightly with a fingertip.
Cut around warm cake 1/4 in from the edges of the pan with a sharp knife.
Invert pan onto a clean towel dusted generously with icing sugar.
Peel off waxed paper.
Gently roll wider length of cake jelly roll style in towel.
Cool rolled and wrapped cake completely on a wire rack.
Make Quick Coffee Cream Filling and Easy Chocolate Butter Frosting.
Spread with Quick Coffee Cream Filling
Place on serving plate.
Cut a 1/2in-or-thicker slice(s) from the ends of the cake roll to use as knot(s) or trimmed limb(s) of cake.
Use Easy Chocolate Butter Frosting to attach these knots and limbs to the cake roll.
Frost cake roll with remaining Easy Chocolate Butter Frosting.
If desired, use the tines of a fork or an icing spatula to make the icing look like realistic "bark."
If desired, sprinkle the ends of the roll and/or the knots/limbs with chopped pistachios, or flaked (or toasted) coconut.
If desired, dust with icing sugar.
If desired, decorate with Make-Ahead Meringue Mushrooms.
Chill until 10-20 minutes before serving time.