In a small bowl, stir together the flour, cornstarch, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or a large bowl using an electric beater, beat the butter on low speed until soft, about 1 minute.
Add the sugar and beat until the mixture becomes fluffy, 3 to 5 minutes. Add the egg, vanilla, and almond extract and continue to beat until the mixture combines well and becomes creamy, 1 to 2 minutes.
Add the flour mixture to the butter mixture and continue to beat until the dough comes together, 1 to 2 minutes. Cover the dough and chill it in the refrigerator for at least 1 hour and up to 2 hours.
Preheat the oven to 350°F and line a baking sheet with parchment paper or a silicone baking mat.
Meanwhile, if using guava paste, use a wooden spoon to break the paste into chunks and melt the chunks in a small saucepan over medium heat until thick, smooth, and glossy, 10 to 15 minutes, stirring occasionally. Remove from the heat.
With your hands, roll 1 to 1½ tablespoons of the dough at a time into balls, arranging them 1 inch apart on the prepared baking sheet.
Using your thumb, press a cavity in the middle of each cookie. Don’t press all the way through. Spoon 1 teaspoon of guava paste into each cavity. It should form a slight mound.
Bake until the cookies barely turn golden, about 25 minutes.
Remove from the oven, transfer to a rack to cool, and sprinkle with powdered sugar.