On goodeggs.com, hover your mouse over the top right corner where it says Hi [Your Name]. A dropdown menu will appear and you can click on Your Orders to view your order history. You'll be able to view your eight most recent orders. Orders placed more than 18 weeks prior will not appear on Your Orders page.
From the Good Eggs app, you can click on the Shop Your Previous Orders banner on the Home screen. Otherwise, you can tap on the You icon and see your five most recent orders.