Baking Challah Close to Shabbat
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Hello
It is forbidden to bake anything close to Shabbat unless its "surface has crusted" before Shabbat, which is a degree of baking sufficient for eating under pressing circumstances.
Regarding other dishes, the degree is that it should be cooked "like the food of Ben Drosai" before Shabbat - meaning cooked to a degree that it can be eaten under pressing circumstances.
If it has not been prepared to this degree, it is forbidden to leave food or a dish - unless the fire is raked or covered, or other permissions apply.
In our times, for dishes - it suffices that the fire is covered with a metal sheet, or that it is placed on a hotplate.
In the oven - there are not so many effective permissions.
Moreover, opening an oven while it is operating poses the issue of turning the thermostat on and off.