What is a style of vegetable preparation in which the covered with topping such as sauce cheese and or bread crumbs browned under broiler salamander?

The style of vegetable preparation you're describing is called Gratin.

A gratin is a dish of vegetables, often layered with cheese, breadcrumbs, and sometimes other toppings like cream or sauce. It's then browned under a broiler or salamander, giving it a crispy, golden-brown crust.

Some common examples of gratins include:

* Potato Gratin: Thinly sliced potatoes layered with cheese, cream, and seasonings.

* Broccoli Gratin: Tender broccoli florets layered with cheese sauce and breadcrumbs.

* Cauliflower Gratin: Roasted cauliflower florets tossed with cheese, garlic, and herbs.

The key elements of a gratin are the layered vegetables, the topping of cheese and/or breadcrumbs, and the browning under a heat source.