Hamburgers in the broiler come out fine, they're not gray and they taste decent. Cooking times depends on how big the patties are. If you broil them you will get a nice bit of char on the outside and still retain the juices. You do not want to cook them on anything but broil. 1/3lb patties that are semi thick, I'd say about 5 mins than flip and 4 minutes. check by pressing down lightly, the liquid coming out should be clear not red. When it's clear you're good to eat. I might be a few more minutes, but for my oven an 1.3lb patties 9 is about perfect.
I cook & consume more burgers in a week than most people on here do in a month, maybe 2 or 3. Do not listen to them.
I recommend you try taking 2 smaller patties (1/4lb or so) putting cheese, bacon whatever you want in the middle. And toss the 2nd patty on top, mush the edges down to form 1 big patty and bake. Stuffed burgers OWN!