For the Scallion Pancakes:

1. Make the dough:
   In a large bowl, combine the all-purpose flour and salt. Gradually add warm water, stirring as you go, until the dough starts to come together. Knead the dough on a lightly floured surface for about 5-7 minutes, until smooth and elastic. Cover the dough with a damp towel or plastic wrap and let it rest for 30 minutes.

2. Prepare the pancakes:
   After resting, divide the dough into 4 equal portions. Roll each portion into a ball, then flatten each ball into a small circle about 1/4-inch thick. Brush each dough circle with vegetable oil and sprinkle evenly with chopped scallions and sesame oil (if using). Roll each circle into a cylinder, then coil the cylinder into a ball again. Flatten each ball into a pancake again, making sure the scallions are evenly distributed inside.

3. Cook the pancakes:
   Heat a bit of vegetable oil in a skillet or frying pan over medium heat. Fry each scallion pancake for 2-3 minutes on each side, or until golden brown and crispy. Set aside and keep warm.

For the Sandwich:

4. Cook the bacon:
   In a separate pan, cook the bacon over medium heat until crispy, about 4-5 minutes per side. Drain on paper towels and set aside.

5. Cook the eggs:
   In the same pan, remove excess bacon grease, leaving a little for flavor. Add butter and heat over medium-low heat. Crack the eggs into the pan, seasoning with salt and pepper. Cook to your preferred level of doneness (scrambled or fried). For fried eggs, cook for about 3 minutes on one side, then flip and cook for another 2 minutes or until the yolk is set but still slightly runny.

6. Assemble the sandwich:
   Place a scallion pancake on a plate. Top with two slices of crispy bacon, one cooked egg, and a slice of cheddar cheese. Top with another scallion pancake to complete the sandwich.

7. Serve:
   Slice the sandwich in half, serve warm, and enjoy!