[b]I don't believe there's such a thing as a tomato, cut in half, and cooked under the grill properly, because any grill being used for a catering purpose will be too hot to grill a tomato properly - that is to say, you can get a nice caramelized top, but inside it'll still be cold and hard. You could instead roast it or make it into a confit, but that's a separate task. Thus, to include tomatoes in a cooked breakfast, it's easier to use cherry tomatoes and grill those instead, on a baking tray preferably, and you get all the benefits of the grill without a cold interior.
In a professional kitchen you would have a hotplate with a 'pass' which are normally heated by halogen bulbs and these can get very hot. Years ago when I'd be making up a breakfast buffet (over 20 yrs ago now - fck me I'm getting old) Tomatoes be the first thing I'd put out under the halogen lamps as they'd cook perfectly just on the heat of the lamps - to the exact same type of consistency as they would by if they were roasted in a fan assisted oven at 185c for 20 mins.
Absolutely correct about mushrooms, though. A well-dried, properly-seasoned mushroom is a delight with any salty or savory dish. A breakfast is hugely dimished without them.
I'm straying well off the reservation here but I've often thought that sautéed cabbage with a spritz of lemon would make a fine accompaniment to a breakfast, adding crunch, flavor, and indeed a veneer of health.
I used to cook around 30kg of mushrooms at a time in a great big machine called a 'Bratt Pan' which were fantastic for making just about anything.
I like cabbage, but prefer it raw, shredded with some chopped parsley and lemon juice. Far too many people overcook cabbage which puts me off it.
There's nowhere to defect to anymore.