I've never heard of a dish called "fried egg rice" but it would make me picture rice made (somehow) from eggs which has been fried (similar to "fried rice noodles" being noodles made from rice which are fried). In "egg fried rice", "egg fried" is a compound adjective which describes a specific method of preparation. Other examples of this type of construction would be "pan fried rice" or "home cooked rice". One way to show that "egg fried" is it's own compound would be to try and separate them. For "beautiful American girls", beautiful and American are separate adjectives independently modifying "girls". Hope this helps. This is a bit of a confusing concept :)

Fried rice is a dish of steamed rice stir-fried in a wok, often mixed with other ingredients, such as eggs, vegetables, and meat. When we add eggs to the rice, we will fry the eggs together with the rice. In the expression "egg fried rice" (the correct expression), egg does not modify the word rice but fried does, hence the confusion. The rice dish, with egg added, are both fried, which might make us think that the expression should be written as "fried rice with fried egg" or "fried egg and fried rice". The term "egg fried rice" does not appear to be grammatically correct, and it's not. It is simply a way of shortening (abbreviating) the two expressions "fried rice with fried egg" and "fried egg and fried rice", therefore the expression becomes egg fried rice because fried egg rice makes us think that the rice is made from eggs, and that is impossible because rice is not made from anything except rice, i.e., the rice plant. So, "egg fried rice" needs to be read as or comprehended as "fried egg and rice", but egg fried rice is easier to say. Egg fried rice may also be a direct word-for-word translation of the Chinese name for the dish. In the phrase "beautiful American girls", beautiful and American are both adjectives modifying and describing the noun girls. Now, here's something cool about multiple adjectives, they must be written or spoken in a certain order following the OPSHACOM rule. Look at this funny link: http://www.professorgrammar.com/opshacom1.shtml Egg fried rice would not follow this rule because fried is an adjective BUT egg and rice are nouns. Whew... I'm exhausted now... :)

Look at this page - I suspect your thinking is confused by the wrong rule: http://www.gingersoftware.com/content/grammar-rules/adjectives/order-of-adjectives/