The French culinary term for a dish that has been covered with breadcrumbs or grated cheese and browned is "gratin".
Gratin is a French culinary term that refers to a dish that has been topped with breadcrumbs, cheese, or a mixture of both, and then browned under a broiler or in an oven. The term "gratin" can refer to both the technique of browning a dish in this way, as well as to the dish itself.
To make a gratin, the base of the dish is typically made up of vegetables, pasta, or potatoes, and is then covered with a layer of breadcrumbs, cheese, or a mixture of both. The dish is then baked or broiled until the topping is golden brown and crispy.
Gratin dishes can vary widely in terms of ingredients and flavors. For example, a classic potato gratin might be made with sliced potatoes, cream, and Gruyere cheese, while a vegetable gratin might be made with zucchini, tomatoes, and Parmesan cheese. Gratin dishes can be served as a side dish or as a main course, and are often found on the menus of French and other European restaurants.