In saucepan, bring 1-1/2 cups (375 mL) water, sugar and honey to boil, stirring until sugar is dissolved. Add apricots; reduce heat and simmer over medium-low heat until soft, 5 to 12 minutes. Using slotted spoon, transfer to bowl. Cool apricots and syrup separately. Stir lemon juice, and rosewater (if using) into syrup. (Make-ahead: Refrigerate separately for up to 2 days.)

Semolina Cake: Line bottom of greased 8-inch (20 cm) pan with parchment or waxed paper; set aside. In large bowl, beat egg whites until frothy; beat in cream of tartar until soft peaks form. Beat in sugar, 1 tbsp (15 mL) at a time, until stiff glossy peaks form; set aside. In second bowl, whisk semolina flour with all-purpose flour; set aside.

In separate large bowl, beat together egg yolks and lemon rind until pale, thickened and mixture falls in ribbons when beaters are lifted, 8 to 10 minutes. Sprinkle semolina flour mixture over top; stir in (mixture will be crumbly). Alternately fold in egg white mixture and butter, making 3 additions of egg white mixture and 2 of butter.

Pour into prepared pan; bake in centre of 350F (180C) oven until golden and cake tester inserted in centre comes out clean, 22 to 24 minutes.

Place hot cake in pan on rack; using skewer, liberally poke holes in top. Pour 1 cup (250 mL) of the apricot syrup over cake; let cool completely. Run knife around edge to remove from pan. (Make ahead: Wrap in plastic wrap and store for up to 2 days or freeze in airtight container for up to 1 month.) Cut into wedges. Serve with apricots and extra syrup.

Makes 8 to 10 servings.