Preheat oven to 350°F. Line jelly roll pan with parchment paper.
Beat egg yolks with 1/2 cup sugar until thick and pale, 3-4 minutes.
Whip egg whites with salt to soft peaks. Add remaining sugar, beat to stiff peaks.
Fold cocoa and vanilla into yolks. Fold in egg whites gently.
Spread batter in pan. Bake 10-12 minutes until cake springs back.
Flip hot cake onto powdered sugar-dusted towel. Remove parchment.
Roll cake with towel from short end. Cool completely, about 30 minutes.
Beat butter until creamy. Add powdered sugar, cocoa, and cream. Beat until fluffy, 4-5 minutes.
Unroll cake. Spread with one-third buttercream. Re-roll without towel.
Cut diagonal slice from end, attach to side as "branch."
Frost entire log. Drag fork through frosting for bark texture.
Decorate with mushrooms, cranberries, rosemary, and powdered sugar. Chill 2 hours before serving.