Heat oven to 375.
Grease a 15x10x1 baking or jelly roll pan or spray it with baking spray.
Line it with a waxed or parchment paper rectangle cut 1/2 inch smaller than the pan (14×9).
Grease the paper or spray it with baking spray.
Sift flour, baking powder, and salt into a bowl or onto another sheet of waxed paper and set aside.
In a mixer, beat eggs yolks, lemon juice, and vanilla until thick and yellow.
Add the 1/4 cup sugar and beat on high until dissolved.
Pour mixture into a clean bowl and set aside.
Wash the mixing bowl and beaters.
Beat the egg whites on medium until soft peaks form.
Add the 1/2 c sugar by the tablespoon and beat until stiff peaks form.
Fold the reserved egg yolk mixture into the beaten egg white mixture quickly with the mixer or with a spatula.
Gently and quickly, fold in the flour mixture with a spatula.
Spread batter into the pan as evenly as possible.
Bake 12-15 minutes until center spring back when pressed lightly with a fingertip. [The cake may look a bit bubbly or even mountainous! No worries! It will flatten out with the folding, anyway!]
Immediately loosen the edges of the cake with a knife.
While the cake is still quite warm, 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. You want a long thin roll, not short and thick.
Cool rolled and wrapped cake completely on a wire rack. [You can store the cake like this for up to one day or re-roll the cake in wax paper, wrap wax-paper rolled cake in foil and freeze for 2-3 weeks.]
Unroll your cake from the towel.
[Optional] Using a pastry or basting-style brush, spread the Lemon Soak generously onto the [inside] surface of the roll cake. [I only used about 1/16 of a cup.]
Spread the inside/top surface of the unrolled cake with the Lemon Cream.
Gently re-roll the cake.
Place the filled cake on a 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. Or, if using as a jelly roll, skip to Step 29.
Use the Lemon Mascarpone Icing to attach these knots and limbs to the cake roll.
Frost the cake roll with the remaining Lemon Mascarpone Icing. You do not have to ice the open ends and open knots of the cake. This is a bit tricky, but can be done with a clean icing spreader.
If desired, use the tines of a fork or an icing spatula to make the icing look like realistic “bark.”
If desired, decorate with Make-Ahead Mushrooms, Candied Lemon Slices, and additional lemon zest.
Chill until 10-20 minutes before serving time.