Preheat oven to 325°F. In a large bowl, with a mixer on high speed, beat eggs and sugar until thick and pale yellow (5 to 6 minutes).
In a small bowl, mix flour and baking powder. With mixer on medium speed, gradually add flour mixture to egg mixture in small increments and beat until smooth.
Scrape batter into a buttered 9" x 13" baking pan.
Bake in a regular or convection oven until a toothpick inserted in the center comes out clean, about 30 to 40 minutes.
In a blender, combine condensed milk, evaporated milk, regular milk, and vanilla until well blended.
Use a fork to poke the cake, making small holes (this will allow the milks to absorb better).
Pour the milk mixture evenly over the hot cake, just enough to soak it but not overflowing. Let cool about 15 minutes, then cover and chill at least 3 hours, or up to 1 day.
Before Serving:
In a chilled mixing bowl, beat the heavy cream and the sugar with an electric mixer on high speed until peaks form.
Cut cake into small squares and set inside shot glasses or mini dessert bowls. Top each piece of cake with strawberries. Cover with whipped topping and lemon or lime zest. Serve.