Preheat oven to 400°F. Generously grease a 9-inch by 2-inch inch round cake pan and dust with flour, knocking out excess.

Whisk together flour, almond meal and 1/3 cup sugar in a large bowl. Add the egg yolks, milk, and vanilla, and whisk until combined (batter will be thick). Beat whites in a bowl using an electric mixer at medium-high speed until they hold soft peaks. Slowly add in the remaining 1/3 cup sugar while beating at medium speed, then increase the seed and beat until whites hold stiff, glossy peaks. Stir one third of whites into batter to lighten it, then fold in remaining whites gently but thoroughly. Spoon batter into the prepared cake pan and bake until cake is springy to the touch, and a wooden pick or skewer inserted in the center comes out clean, about 18 minutes. Cool cake in pan on a rack 5 minutes, then invert onto rack and cool 10 minutes.

While the cake is baking, bring water and sugar to a boil in a 1-quart heavy saucepan, stirring until sugar is dissolved. Cool syrup 20 minutes, then stir in lemon juice and almond extract. Place berries in a large mixing bowl and pour syrup over; gently stir to coat the berries. Arrange cooled cake, right side up, on a platter and arrange berries on top; spoon remaining syrup evenly over top, allowing it to soak into the cake.