1. Preheat the oven to 350°F (176°C) and grease a 9×13 cake pan.
2. Combine the flour, baking powder and salt in a medium sized bowl and set aside.
3. Add the butter, sugar and oil to a large mixer bowl and beat together until light in color and fluffy, about 3-4 minutes. Do not skimp on the creaming time.
4. Add the eggs and mix until well combined. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated.
5. Add half of the dry ingredients to the batter and mix until mostly combined.
6. Add the milk and vanilla extract and mix until well combined.
7. Add the remaining dry ingredients and mix until well combined. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated. Do not over mix the batter.
8. Add the batter to the prepared cake pan and spread evenly.
9. Bake for 28-32 minutes, or until a toothpick inserted comes out with just a few crumbs.
10. Poke holes all over the cake. I use a knife sharpening rod, but you could also use something like the end of a wooden spoon or a large straw. The holes can be poked when the cake is warm or after it has cooled.
11. Pour the sweetened condensed milk over the can and spread it evenly so that it can soak into the holes.
12. Add the pureed strawberries, sugar and vanilla extract to a large saucepan. Cook over medium heat, stirring continuously, until it begins to boil. Boil for 1 minute
13. Remove the strawberry sauce from the heat and pour it over the cake, spreading it evenly and letting the juices soak down into the holes. There will still be a thin layer of the sauce on top of the cake.
14. Cover the cake and refrigerate cake until completely cooled.
15. To make the whipped cream, add the heavy whipping cream, powdered sugar and vanilla extract to a large mixer bowl. Whip on high speed until soft peaks form.
16. Add the cream cheese and whip on high speed until stiff peaks form and whipped cream is smooth.
17. Set aside about 1 cup of the whipped cream and then spread the rest evenly onto the cake.
18. To finish off the cake, top it with swirls of the remaining whipped cream and some additional strawberries. I sliced some strawberries very thinly and added a layer of those on top of the cake, then added the piped whipped cream.
19. Store the cake in the fridge until ready to serve. Allow the cake to sit out for about 45 minutes before serving. Serve the cake cool, but not cold (it just tastes best that way). The cake is best when stored well covered and eaten within 3-4 days.