Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking dish.
In a medium bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Set aside.
In a large bowl, beat the egg yolks with 3/4 cup of granulated sugar until the mixture is pale and thick, about 3-4 minutes.
Add the vegetable oil, whole milk, and 1 teaspoon vanilla extract to the egg yolk mixture and mix until combined.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined.
In a separate clean bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/4 cup granulated sugar and continue beating until stiff peaks form.
Gently fold the beaten egg whites into the chocolate batter in three additions, being careful not to deflate the mixture.
Pour the batter into the prepared baking dish and smooth the top with a spatula.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
While the cake is still warm, poke holes all over the surface using a fork or skewer.
In a medium bowl, whisk together the evaporated milk, sweetened condensed milk, and 1/2 cup whole milk.
Slowly pour the milk mixture evenly over the cake, allowing it to soak in.
Refrigerate the cake for at least 4 hours or overnight to absorb the milk mixture fully.
Before serving, make the whipped cream by beating the heavy whipping cream, powdered sugar, and 1 teaspoon vanilla extract until stiff peaks form.
Spread the whipped cream evenly over the soaked cake.
Sprinkle the semisweet chocolate shavings on top as a garnish.
Slice and serve chilled.