Whisk the eggs in a small bowl. Stir in the salt and pepper.
Spread butter on one side of each slice of bread and set aside.
Heat the oil in a large skillet over medium heat. Add the eggs and scramble until cooked through. Transfer the eggs to a plate.
Place one slice of bread in the same skillet, buttered side down.
Top the bread with the scrambled eggs and shredded cheddar cheese. Place the remaining slice of bread on top, buttered side up.
Cook for 3–4 minutes, or until the bottom is golden brown. Flip the sandwich and cook for another 3–4 minutes, until golden brown and the cheese is melted.
Remove from the skillet, cut in half, and serve immediately.
Notes
Use your favorite type of cheese in place of cheddar, if desired.This sandwich is best served fresh.Store leftovers in an airtight container in the refrigerator for up to 5 days.