For the filling: In a small bowl whisk the eggs and the sugar. Slowly add the flour until the mixture is unified.
On medium heat, bring the milk and butter to a gentle boil. Slowly whisk in the warm milk into the egg mixture. Do this slowly so as not to cook the eggs. When mixture is well blended return to the saucepan and slowly add the marzipan, stirring constantly. Add the butter, and both extracts. Remove from heat and stir about 2 more minutes. Place in a bowl and refrigerate for about 3 hours.
For the frosting: In a small saucepan on medium heat bring cream to a gentle boil. Add the butter. When butter is melted, slowly begin to add the chocolate about ¼ at a time.
Stir constantly until chocolate is thoroughly melted. Place in a small bowl and refrigerate for up to 2 hours.
For the cake: Preheat over to 350F.
Line a jelly roll pan with parchment paper and rub with butter.
Separate the eggs and set the whites aside.
In a bowl, whisk together the egg yolks, sugar and flour. Add the salt and almond extract and melted butter(at room temperature).
Place the whites in a large bowl and using an electric mixer beat the whites until they form stiff peaks. Slowly, using a spatula, mix in the egg yolk mixture.
Spread batter on parchment paper and bake for about 20 minutes.
Remove from oven and wait about 5 minutes.
Invert onto a lightly floured kitchen towel.
Gently pull parchment off cake and allow to cool slightly (about 10 minutes).
Using a wide spatula, spread almond filling all over the cake.
Starting at the bottom, carefully roll up and place seam side down on a large serving platter.
To make branches, slice off about ½" from either end of the cake and "glue" to cake using the chocolate frosting.
Using another spatula spread chocolate frosting over the rolled cake, trying to achieve texture (like a log). If the texture appears a bit too smooth, use the tines of a fork to create texture.