Hell yes! When I lived in LA I’d get a burger with egg and bacon at Fatburger all the time. None around here unfortunately. 
My Australian friend calls it ketchup, but she might have spent too much time in the states.
That sounds good. I rarely make burgers at home, but now I want one! I just got some buns, though…and I bet I’ve got frozen ground beef, and I KNOW I have eggs! Maybe tomorrow for dinner!