If pizza can be made on the BBQ, it can be made on the stove, I'm sure.
Whether your stove is gas or electric, I would try this:
Saute or microwave your misc toppings, such as onions peppers and
mushrooms, with preferred seasonings. This will release the juices that
will make your pizza soggy, which you can drain and/or mix with your fave
pizza sauce.
Lightly toast a thinner pizza dough in the pan on one side only to precook
it (try coating it with olive oil garlic and other seasonings). Flip the
dough, and to the toasted side, add your sauce, toppings, and cheese. Cook
to melt the cheese, but avoid covering it which will steam it and create a
soggy mess. If your burner is hard to control, move your pan around or even
off the burner to prevent burning.
The key here is to reduce the thickness of the dough, which takes more time
to cook, and the layer of toppings, which block the heat from melting the
cheese.
Experiment and let us know how it worked out!
Catherine