For the milk mixture: Pour condensed milk into large microwave-safe bowl and cover tightly with plastic wrap. Microwave on low power, stirring and replacing plastic every 3 to 5 minutes, until slightly darkened and thickened, 9 to 15 minutes. Remove from microwave and slowly whisk in evaporated milk, 1 cup cream, and 1 tsp vanilla. Let cool to room temperature.
For the cake: Adjust oven rack to middle position and heat oven to 325 degrees. Grease and flour 13 by 9-inch baking pan. Whisk flour, baking powder, salt, and cinnamon in bowl. Heat butter and milk in small saucepan over low heat until butter is melted; set aside off heat.
With electric mixer on medium speed, beat eggs in large bowl for about 30 seconds, then slowly add sugar until incorporated. Increase speed to medium-high and beat until egg mixture is very thick and glossy, 5 to 7 minutes. Reduce speed to low and slowly mix in melted butter mixture and 2 tsp vanilla. Add flour mixture in three additions, scraping down bowl as necessary, then mix on medium speed until fully incorporated, about 30 seconds. Using rubber spatula, scrape batter into prepared pan and bake until toothpick inserted into center comes out clean, 30 to 35 minutes. Transfer cake to wire rack and let cool 10 minutes.
Using skewer, poke holes at 1/2-inch intervals in top of cake. Slowly pour milk mixture over cake until completely absorbed. Let sit at room temperature 15 minutes, then refrigerate uncovered 3 hours or up to 24 hours.
For the frosting: Remove cake from refrigerator 30 minutes before serving. With electric mixer on medium speed, beat 1 cup heavy cream, corn syrup, and 1 tsp vanilla to soft peaks, 1 to 2 minutes. Frost cake and slice into 3-inch squares. Serve. (The assembled cake can be refrigerated for up to 3 days.).