Preheat the oven to 350ºF. Butter cake pan and line it with parchment paper. Sift together the flour, cornstarch, ground cinnamon and baking powder and set aside.
In a bowl using an electric mixer, beat the butter and sugar on medium speed, scraping down the sides of the bowl, until light and fluffy, 3 to 4 minutes.
Add the eggs, vanilla, milk, cheese and beat until smooth and blended, about 1 minute more. Reduce the speed to low and add the flour mixture until smooth. Transfer half of the batter to the prepared pan.
Place the guava paste pieces over the batter, spreading it evenly.Top with the remaining batter and bake for about 30 minutes or until a toothpick inserted into the center comes out clean.