[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.
Freed us eventually | Just need to be happy.