Preheat oven to 325°F. Prepare 2 - 6 in. round pans with parchment paper. Do not spray the pans.
In large bowl, whip egg whites with electric mixer on high speed until foamy. Add cream of tartar and 1/4 cup sugar, 1 tablespoon at a time, and continue whipping until glossy and whites hold stiff peaks.
In large bowl, sift together flour, remaining 1/4 cup sugar, baking powder, ground ginger and salt.
In small bowl, whisk together milk, egg yolks and ginger. Stir into flour mixture until just combined. Fold 1/3 of beaten egg whites into yolk mixture to loosen, then fold in remaining egg whites until no streaks remain. Divide evenly into prepared pans.
Bake 23-27 minutes or until toothpick inserted in center comes out clean. Cool 10 minutes on cooling rack; remove from pan and cool completely.
In medium saucepan, whisk together juice and cornstarch until completely dissolved. Whisk in sugar and salt. Cook over medium heat until steaming. While whisking, slowly pour half of hot liquid into egg yolks to warm them gently. Reduce heat to medium low and pour back into saucepan. Continue cooking, stirring constantly, until mixture thickens and just boils.
Remove from heat and pass through a fine mesh strainer. Add butter and tangerine zest; stir until butter melts and is completely incorporated. Cover with plastic wrap and refrigerate until completely cool.
Green Tea Icing
In double boiler, combine egg whites, granulated sugar, matcha powder and salt. Whisk constantly over simmering water until mixture reaches 150°F on a thermometer. Transfer to large bowl; whip at high speed with electric mixer until mixture cools to room temperature. Switch to paddle attachment on mixer. While beating at medium speed, add butter, one piece at a time, scraping bottom and sides of bowl as necessary.
To assemble cake, cut each cake layer in half horizontally. Place the bottom cake layer, cut side up, on cake board. Pipe a dam of icing about 1/4 in. from outside edge of cake. Fill with tangerine curd. Place next cake layer on top. Gently press into place and repeat, piping dam and filling. Refrigerate at least 4 hours to set cake. Ice top and sides of cake. Refrigerate until ready to serve.