To a small saute pan (8 inches or so), add the kimchi. Cook about 3 minutes over medium-high heat, long enough to get any liquid out. Set aside.
To the same pan, add a thin layer of oil. Pour the beaten egg in and quickly move it around in the pan so that it coats the entire bottom in a thin layer. Once the egg is no longer runny, to one half of the omelet, add the crumbled bacon, the soft cheese and scallions. Fold over into a half moon shape and set aside.
Spread 1/2 TB mayo on each slice of bread and sprinkle with 1/2 the sesame seeds.
Spread 1/2 of the grated cheddar on one slice of bread (the side without mayo), then top with the omelet and kimchi. Add the remainder of the shredded cheese, and top with the second slice of bread, mayo side up and press down.
To a skillet (if you need to add the 1 tsp butter to not make it stick, go ahead) or a well-oiled grill pan or griddle (the butter may not be needed) over low heat, place the sandwich. Press down using something heavy (like another skillet) and let cook 3-4 minutes.
Carefully flip the sandwich and cook another 3 minutes on the other side until the bread is toasted.
Serve immediately. Enjoy!