Strawberry and Cream Cake with Cardamom Syrup

Put oven racks in upper and lower thirds of oven and preheat oven to 350 °F. Butter cake pans. Line bottom of each with a round of parchment paper, then butter parchment and dust cake pans with flour, knocking out excess. Whisk together yolks, 1 cup sugar, milk, vanilla, and zest in a large bowl until smooth. Whisk in flour and salt until combined (batter will be thick). Beat whites with a pinch of salt in a bowl using an electric mixer at medium-high speed until they just hold soft peaks. Add remaining 1/2 cup sugar, a little at a time, beating at medium speed, and continue to beat until whites hold stiff glossy peaks, about 2 minutes more. Fold about one third of whites into batter to lighten, then fold in remaining whites gently but thoroughly. Divide batter among cake pans and bake, switching position of cake pans halfway through baking, until cakes are springy to the touch and a wooden pick or skewer inserted in center of each comes out clean, 20 to 25 minutes. Cool cakes in pans on racks 10 minutes, then invert onto racks. Carefully peel off parchment, then cool cakes completely.