In a pot over medium heat, add ½ cup water and bring to a boil. When water begins to boil, add brown sugar and stir until it melts. Remove from heat and set aside.
Place ¾ cup of the glutinous rice flour in a mixing bowl then add melted sugar while still warm. Mix well until well incorporated and no traces of flour left.
Then the ¼ cup glutinous rice flour until dough forms. Pour 1 tsp cooking oil and knead some more until oil is absorbed in the dough. Let it rest for 15 - 20 minutes.
When dough is rested. Roll the dough into a log approximately 12 inches in length. Cut into 12 equal parts. Take a piece of rolled dough and create a hole to place the filling in. Put 1½ tsp purple yam filling on in the hole you made.
Seal all the dough making sure there are no cracks to avoid purple yam spilling out. Roll it on your palm until it's perfectly round. Do with all the remaining pieces of dough.
In a small bowl, dissolve 1 tbsp of glutinous flour in ½ cup water. In a different bowl place sesame seeds. Dip buchi one at a time in the bowl with flour-water mixture then transfer in bowl with sesame seeds and dredge the buchi, making sure all of the dough is covered with sesame seeds.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Deep fry the dough balls in batches until golden brown. When done, let rest to cool down and serve. Bon Appetit!