In a bowl, add tapioca starch and cocoa powder. Mix to combine.
Scoop out 3 tablespoons from the flour mixture and add them to a small bowl. Add 3 tablespoons of water, then stir until smooth to create a starch slurry.
Add 2 tablespoons of dark brown sugar and 3 1/2 tablespoons of water to a small saucepan. Place it over medium heat and bring to a boil, then immediately lower to low heat. Add the tapioca starch slurry while constantly stirring for 10-20 seconds until the mixture starts to thicken. Remove from the stove immediately.
Gradually add the remaining flour into the wet cooked flour mixture (2-3 tablespoons each time) and use a wooden spoon to incorporate. Once the wet flour mixture is fully coated with the raw flour, you can use your hand to knead into a soft, smooth, slightly sticky and bouncy dough.
Lightly dust a clean surface. Press the dough into a flat disk and lightly dust both sides with tapioca flour. Cut into strips.
Roll each strip into a thin log and then cut into small pieces. Then roll each piece into tapioca pearls. Cover the portion of dough that hasn't been used to avoid drying it out.
You may want to lightly dust the pearls to avoid them from sticking to each other. At this point you can freeze them or cook them right away.
Bring a pot with plenty of water to a boil and then add the boba pearls. Maintain a rolling simmer and cook for 10-12 minutes or until they are fully cooked. Boiling time will depend on the size of the pearls. Mine are slightly smaller than green peas.
While cooking the pearls, add dark brown sugar and water for the syrup to a saucepan. Bring to a boil and simmer for 1-2 minutes. Then transfer to a container to cool down.
Once the pearls are fully cooked, transfer them to a bowl with cold water. Then drain and add them to the brown sugar syrup. You can use them now or store in the fridge up to 2 days. Remove from the fridge and microwave briefly until they are bouncy and chewy again.