Peel the potatoes and cut them into evenly sized 1 to 2-inch chunks.
Place the potato chunks in a medium pot and cover with cold water. Add 1 teaspoon salt to the water if desired.
Bring to a boil over medium-high heat, then lower the heat and simmer for 15 to 20 minutes, or until fork-tender.
Drain the potatoes well.
Measure about 850g boiled potatoes, or around 4 cups mashed potatoes, and transfer them to a large mixing bowl.
Mash the potatoes until smooth and free of lumps.
While still warm, add glutinous rice flour, cornstarch, shredded cheese, salt, and pepper.
Mix and knead until a smooth dough forms.
Line a rectangular pan or dish with plastic wrap. Transfer the dough into the pan and press evenly into a uniform layer.
Cover and freeze for 30 minutes to firm the dough.
Remove the dough from the freezer, turn it onto a cutting board, and peel away the plastic wrap.
Cut into 8 sticks, about 1 x 1 x 6 inches each. For a crispier finish, lightly press lines onto the surface with the back of a knife.
Heat oil to 320°F (160°C).
Fry the Potato Cheese Sticks for 5 minutes until lightly golden. Remove and let them rest on a cooling rack.
Increase the oil temperature to 350°F (175°C).
Fry again for 30 seconds to 1 minute, until golden brown and crispy.
Remove and drain on a rack or paper-lined plate.
Sprinkle with salt and chili pepper powder, or serve with ketchup while hot.