Does the skin heal better when our bodies rest from eating or when we eat a lot of food/nutrients?

Balance. There needs to be a good balance. Eating too much sugar can impede wound healing, for example, but not having enough protein can also be bad. As with most things, a health moderation is best.
Adequate nutrition. The keys to wound healing are multifactorial. Wounds need to be clean, warm, moist, and have an adequate vascular supply (nutrients and oxygen supply). Affecting any one of these can affect the ability of the wound to heal itself. That being said, nutrition is important because it supplies nitrogen (in the form of proteins) that is essential for tissue repair and maintenance.
Eat. To heal well, our bodies need to lay down many components which are aided by appropriate intake of vitamins, minerals, protein etc. A deficiency, such as that caused by intentional strvatio.