1. Heat oven to 375 degrees F. Coat a 15 x 10 x 1-inch jelly-roll pan with nonstick cooking spray. Line pan with waxed or parchment paper. Coat with spray.
2. Sift together cocoa, flour, cinnamon, ginger and nutmeg.
3. Beat egg whites with cream of tartar in bowl until frothy. Gradually beat in 1/4 cup of the brown sugar; beat until stiff peaks form.
4. Using same beaters with mixer on high, beat yolks in second bowl with remaining 1/3 cup brown sugar until thick, 5 minutes. Fold cocoa mixture into yolks. Fold yolk mixture into whites. Pour into pan, spreading evenly.
5. Bake at 375 degrees F for 14 to 16 minutes, until center springs back when gently pressed.
6. Sift confectioners' sugar over a clean kitchen towel. Immediately invert cake onto towel; remove pan and paper. Dust confectioners sugar onto cake. Starting from long side, roll cake up inside towel jelly-roll style. Cool, seam-side down, on rack.
7. Once cake has cooled completely, prepare Filling. In medium-size bowl, combine ice cream, ground cinnamon and nutmeg. Beat with an electric mixer until spices are evenly distributed and ice cream is a good spreading consistency. Unroll cake. Working quickly, spread with Filling. Gently reroll cake without towel. Place, seam-side down, on a large platter and freeze for at least 3 hours.
8. Prepare Frosting. Heat cream just until steaming. Pour over chocolate in a medium bowl and let stand 5 minutes. Beat until smooth. On low speed, beat in butter and confectioners' sugar. Continue beating, on high, until smooth and good spreading consistency, about 6 minutes. Remove cake from freezer and cut off one end of cake on the diagonal. Reserve end to use as "knot." Place "knot" on top of log (see photo). Trim uncut cake end to expose filling, making a parallel diagonal cut. Spread frosting over log and "knot," leaving log ends exposed. For bark effect, run tines of fork over frosting. Return to freezer and freeze at least 3 more hours. Slice and serve.