Grease a 9-inch (23-cm) fluted cake pan; sprinkle with fine breadcrumbs.
Preheat oven to 375°F (190°C).
To make cake, beat butter and ground almonds in a large bowl.
Stir in egg yolks, lemon peel and vanilla.
Beat egg whites until stiff; carefully fold in sugar.
Fold egg white mixture into butter mixture.
Sift flour and cornstarch together.
Fold into mixture.
Turn batter into prepared cake pan; smooth the surface.
Bake 50 to 60 minutes or until a wooden pick or skewer inserted in center comes out clean.
Remove cake from pan; cool slightly on a rack.
To make frosting, warm apricot jam and press through a strainer to obtain jelly.
Brush apricot jelly over warm cake.
Let stand 30 minutes.
Combine powdered sugar, lemon juice and water in a small bowl.
Spread frosting over cake.