Heat a nonstick skillet over medium heat and melt 1 tbsp of butter. Scoop about 2/3 cup of egg-veggie mixture onto the pan and shape it into the size of the bread. Cook until the bottom is golden brown, then flip and cook the other side. Repeat for the rest of the mixture.
In a now-empty skillet, melt 1 tbsp of butter and toast bread until lightly browned.
Assemble the sandwich. Drizzle ketchup on top of the egg patty and sprinkle some sugar if you'd like.