To prepare sorbet, pour 3/4 cup hot water over 6 tea bags in a bowl; steep 5 minutes. Remove and discard tea bags; cool tea to room temperature.
Combine 1 1/2 cups water, 1 cup sugar, and honey in a small saucepan; bring to a boil. Cook until sugar dissolves; remove from heat. Pour sugar mixture into a medium bowl, and stir in brewed tea. Cover and chill.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 3 hours or until firm.
Preheat oven to 350º.
To prepare cake, coat the bottom of a 9-inch springform pan with cooking spray. Line bottom of pan with wax paper; coat wax paper with cooking spray.
Pour 1/2 cup hot water over 7 tea bags in a bowl; steep 5 minutes. Remove and discard tea bags; cool tea to room temperature. Set aside.
Combine the almonds, 2 tablespoons sugar, cornstarch, and salt in food processor; process until finely ground (about 1 minute).
Place egg yolks in large bowl; beat with mixer at high speed for 2 minutes. Gradually add 14 tablespoons sugar, beating until thick and pale (about 2 minutes). Place egg whites in large bowl. Using clean, dry beaters, beat egg whites with mixer at high speed until foamy. Add cream of tartar; beat until stiff peaks form. Gently fold egg whites into egg yolk mixture. Gently fold almond mixture and brewed tea into egg white mixture. Spoon batter into prepared pan.
Bake at 350º for 30 minutes or until cake is lightly browned and a wooden pick inserted in center comes out clean. Cool cake completely in pan on a wire rack. Remove sides from springform pan. Loosen bottom of cake from pan using a spatula. Carefully remove and discard wax paper. Serve cake with sorbet.