Prepare the Dough: In a large bowl, combine the all-purpose flour, sweet rice flour, yeast, sugar, and salt.

Add Wet Ingredients: Gradually add the lukewarm water and oil to the dry ingredients, mixing until a shaggy dough forms.

Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or until smooth and elastic. If the dough is too sticky, add a little more all-purpose flour, 1 tablespoon at a time.

First Rise: Place the dough in a lightly oiled bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1 hour, or until doubled in size.

Prepare the Filling: While the dough is rising, prepare the cheese filling by combining the mozzarella cheese, cheddar cheese, sugar, and salt in a bowl. Mix well.

Divide the Dough: After the dough has risen, gently punch it down to release the air. Divide the dough into 6 equal portions.

Shape the Hotteok: Lightly grease your hands with oil. Take one portion of the dough and flatten it into a 4-inch circle. Place about 2-3 tablespoons of the cheese filling in the center of the circle. Gently bring the edges of the dough up and pinch them together to seal the filling inside. Be sure to seal it well to prevent the cheese from leaking out during frying. Repeat with the remaining dough portions.

Fry the Hotteok: Heat about 1/4 inch of vegetable oil in a large skillet over medium-low heat. Once the oil is hot, carefully place the hotteok in the skillet, seam-side down.

Flatten and Cook: Using a spatula or a hotteok press (if you have one), gently flatten each hotteok to about 1/2 inch thickness. Cook for 3-4 minutes per side, or until golden brown and the cheese is melted and gooey. Adjust heat as needed to prevent burning.

Serve: Remove the hotteok from the skillet and place them on a paper towel-lined plate to drain excess oil. Serve immediately while hot and the cheese is still melty.