The traditional Egyptian cookie eaten during Eid al-Fitr is kahk.
Kahk is a round, crumbly shortbread biscuit made chiefly with flour, ghee and sugar. It is commonly dusted with powdered sugar and may be plain or filled with dates, nuts, pistachios, walnuts, lokum or ajamiya, a honey-and-nut mixture.
The cookie has deep roots in Egyptian food culture. Accounts and surviving artistic evidence connect forms of kahk with ancient Egypt, while its role in Eid celebrations became especially prominent under the medieval Muslim dynasties. During the Fatimid period, rulers famously sponsored large-scale production and distribution of kahk for the public.
Kahk is often prepared communally, exchanged as a gift and stamped with decorative wooden or ceramic molds. Maamoul is the tempting alternative in this question, but it is a related filled pastry associated especially with the Levant; it is not the specific Egyptian Eid cookie named here. Kahk is also served at some Egyptian Christian celebrations, including Christmas and Easter.