For the pao de queijo: Preheat the oven to 400 degrees F.
Place the tapioca flour in the bowl of a stand mixer fitted with a paddle attachment. Meanwhile, in a saucepan over medium heat, heat the milk, water, oil, salt, and sugar until simmering. With the stand mixer running on low, incorporate the hot milk mixture into the tapioca flour. Once incorporated, add eggs, one at a time, and continue to mix. Add the cheeses, a little at a time, and mix until incorporated.
Divide dough between the cups of a 24-cup mini muffin pan. Bake until bread is golden brown and puffed, 10 to 12 minutes.
For the guava sauce: In a small saucepan over medium-low heat, add guava paste. Add water, a little bit at a time, breaking up the guava paste with a heatproof rubber spatula. Cook until it takes on a sauce-like consistency.
Serve the pao de queijo with some of the guava sauce drizzled on top.