Preheat the oven to 350°F.
Whisk together flour, salt and baking powder until thoroughly combined and set aside.
Crack eggs into the bowl of a stand mixer fitted with a whisk attachment, or into a medium bowl if using hand beaters. Beat the eggs on medium speed for 1 minute. With the mixer running, slowly stream the sugar in.
When the sugar is completely in, turn the speed to high and beat for about 7 minutes. The mixture should be light and fluffy.
Combine the milk, butter and guava paste in a saucepan and gently heat over medium low until completely melted. Do not let it overheat or simmer. Strain. Add vanilla and oil and whisk to combine. Set aside but do not let it cool off too much (do not do this ahead of time).
Add the flour mixture in three parts to the egg mixture, mixing just until almost combined. If you still see flour, finish mixing by hand by folding the batter with a rubber spatula.
Remove two large spoonfuls of batter and add it to the milk-butter-guava mixture and whisk to completely combine. This tempers your milk mixture so that it does not cook your egg mixture.
Pour the milk-butter-guava mixture into the rest of the egg mixture with the beaters running on low. Continue beating just 10-15 seconds more until combined.
Pour into the prepared pan and spread out with an offset spatula. Bake for 15-20 minutes or until a toothpick inserted comes out clean. Remove from the pan and let cool completely on a wire rack.
Punch out as many circles of cake with a 3-inch round cutter as you can. I ended up with 12.