This is the best <I>tasting</I> grilled cheese I make, but it's one that is decadent and should be had sparingly:

I either saute shallots and red peppers, or caramelize onions and saute red peppers to add to the grilled cheese. I just add light amounts of salt and pepper while doing this, no other seasoning.

In terms of cheese choices, I find fontina works really well.

You can slather one of the slices of bread in pesto. This adds good flavor, and you can do alternate pestos, as opposed to the classic. There's a walnut and kale pesto with asiago that tastes delicious here.

I assemble all this into bread, typically a good sandwich white, or a sourdough, then I use mayo instead of butter to grill the sandwich. This mayo instead of butter makes a huge difference actually, so I recommend it no matter what you put inside.

You can use a sandwich press, but I prefer a single sandwich stove top press that I have. Let's be control the browning very well, and I can stop just as the cheese is deliciously melted.

Another combo I'm fond of has no veggies, and instead of pesto, I use a fig jam, and a spicey coriander chutney on either slice. The sweet and spice combo, with a mild cheese, goes really well.

As for what else can be grilled, one of my favorites, and this is fairly healthy, is to make grilled halloumi and pineapple skewers. Slice up the halloumi cheese and pineapple, give them a light dusting of za'atar (this is a Mediterranean spice mi and olive oil, skewer and then grill. You can also do peaches or watermelon instead of the pineapple, or mix in the fruits.

This is also great to barbecue, and if you use smaller skewers/toothpicks, can be served as canapes if you're entertaining (which, granted, you may not be, in the middle of all this nonsense).