How can I increase my progesterone levels naturally through food?

Don't! There are no foods that stimulate progesterone. Further, foods traditionally claimed to contain Progesterone such as mexican yams are unregulated, may contain progestins but not progesterone, and do not have a progestogenic effect. Many have an estrogenic effect! if you have a true need for additional progesterone, which most women don't, talk with a knowledgeable doctor.
Diverse diet. Progesterone is formed internally from cholesterol in the ovary. Progesterone levels depend on effective ovulation. Low fat diets can lower Progesterone levels. Normal fat levels, including essential oils (dha, omega-3) are helpful to maintaining good ovulation.