In a saucepan over medium high heat, add water, sugar and bring the mixture to a boil allowing the sugar to dissolve, then turn off the heat.
In a bowl, add glutinous rice flour and create a well in the center and slowly add half of the hot water-sugar mixture.
Stir to combine until you reach the consistency of wet but not overly sticky. rest for 15 minutes.
Scoop out 1-ounce of dough and form it into a ball.
Continue rolling until the ball is smooth without cracks.
Place in a rack and cover with a cling film.
Using your thumb, make an indention at the center of the dough and scoop out a quarter teaspoon of ube halaya and place it at the center of the dough. Then gather the edges of the dough around the filling and pinch to seal.
Roll the dough repeatedly until a smooth ball forms with no opening.
Place sesame seeds on a plate.
Gently dip the balls into a bowl of water, then roll the moist dough balls in the sesame seeds.
Repeat the process with the remaining dough and fillings.
In a pot, heat the oil until it reaches 325 degrees Fahrenheit.
Fry the dough balls until golden brown for 5-7 minutes.
Move the Buchi from time to time to prevent overcooking.
Remove and transfer to a wire rack to cool and drain excess oil.