Combine the mashed ube, coconut milk, brown sugar, ube extract, and salt. Mix until smooth.
Toast the glutinous rice flour over medium heat, stirring often, until light brown and nutty (about 20 minutes). Set aside ½ cup for coating.
Reduce the heat to low and stir in the tapioca flour for about 2 minutes. Turn off the heat.
Prepare a piece of parchment paper (12x12 inches) and dust it with some of the reserved toasted flour.
Pour the wet mixture into the pan with the flour. Cook over medium heat, stirring and folding for about 10 minutes until thick, sticky, and harder to stir.
Transfer the warm mixture onto the prepared parchment paper and spread to about ½ inch thick.
Dust the top with toasted flour, cut into pieces, then roll each piece in more toasted flour. Shake off any excess.