This early phase I trial studies how well ketogenic diet with letrozole works in treating patients with estrogen receptor positive breast cancer. Estrogen receptor positive breast cancer has special proteins on it, called estrogen receptors, that allow it to grow when exposed to estrogen. A ketogenic diet (low calorie, low carbohydrate) may help normalize abnormally high insulin levels that in turn may slow the growth of cancer cells. Letrozole may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. The purpose of this study is to learn if the combination of a 2 week ketogenic diet in combination with letrozole can help slow the growth of tumors.