Preheat oven to 350 degrees F. Butter and flour bottom and sides of 8x8x2" metal cake pan. Set aside.
Whisk 1 1/2 cups flour, baking powder, and cinnamon in a large bowl. Using an electric mixer, beat egg whites in another large bowl until firm peaks form, 7-8 minutes. Gradually beat in sugar. Add egg yolks one at a time, beating to blend between additions. Beat in 2 teaspoons vanilla. Add flour mixture in 3 additions, alternating with milk in 2 additions, beginning and ending with flour mixture. Pour batter into pan; smooth top.
Bake cake for 25 minutes. Reduce heat to 325 degrees F; continue baking until cake is golden brown and middle springs back when pressed, 20-25 minutes more. Let cake cool in pan for 15 minutes. Invert cake onto a wire rack set inside a rimmed baking sheet.
Whisk 1/2 teaspoons vanilla, evaporated milk, and remaining ingredients in a medium bowl. Poke holes all over top of cake with a skewer. Slowly drizzle half of sauce over cake, letting liquid soak in before adding more. Let cake sit for 10 minutes.
Invert a plate on top of cake. Lift rack and gently invert cake onto plate. Drizzle remaining sauce over. Spoon any liquid collected on sheet over cake.