Make the syrup ahead. Combine the sugar, lemon zest and juice, and water in a saucepan. Bring to a boil, simmer for 5 minutes then add the almond extract. Remove and chill overnight.
Line a 10-inch-square cake pan, that is at least 3-inches deep, with parchment. Sift together the flour and baking powder, then stir in the semolina. Beat the egg yolks, sugar, olive oil, lemon zest, and almond extract together until pale and creamy. Beat in the flour mixture, splashing with orange juice to moisten it.
Wipe a mixing bowl with a cloth moistened with vinegar, then put in the egg whites. Beat with the cream of tartar until stiff peaks form, then fold into the batter. Pour into the pan and sprinkle with the almonds.
Bake in an oven preheated to 350 F for about 45 minutes until golden brown. Remove from the oven and, while still hot, cut into squares. Slowly pour the chilled syrup over it.
Makes 16 slices
Karen Mintzias
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