Heat the oven to 350 °F. Have an ungreased baking pan ready so the sponge can grip the sides as it rises.
Whisk the flour, baking powder, and salt in a medium bowl, then place the egg yolks and whites in separate mixing bowls. Keep the whites free of yolk so they can whip to full volume.
Beat the yolks with 3/4 cup sugar on high until thick, pale, and able to fall in a slow ribbon, then mix in 1/3 cup milk and vanilla. Fold the yolk mixture into the dry ingredients only until no dry flour remains.
Whip the egg whites on high, gradually adding the remaining 1/4 cup sugar as they build volume. Stop at glossy stiff peaks that stand upright, then fold them into the batter from the bottom upward.
Spread the batter evenly in the ungreased pan and bake for 25 to 35 minutes. The top should feel springy and dry to the touch, and a toothpick in the center should come out clean.
Cool the cake completely, then stir together the evaporated milk, sweetened condensed milk, and 1/4 cup whole milk. A fully cooled sponge stays intact when the liquid reaches its air pockets.
Use a fork to pierce the entire cake, then slowly pour the milk mixture over the top, including the edges. Refrigerate for at least 1 hour or overnight so the sponge can absorb the soak.
Whip the heavy cream with powdered sugar and vanilla until stiff peaks form, then spread it over the chilled cake and finish with cinnamon. The cream should hold soft, defined swirls rather than slide across the surface.