Learn Farsi: پرنده‌شناس به منقار درشت و زرد پرنده خیره شد. - The ornithologist stared at the bird's large and yellow beak.

This showcases exactly what you are learning in this lesson! Normally, a chain of multiple adjectives uses an Ezafe after every word (like منقارِ درشتِ زرد). However, when you link modifiers with و (and), you drop the Ezafe right before the و. The head noun (منقار) still takes its Ezafe to introduce the phrase, but درشت does not.

Wait, if we drop the Ezafe before و, why is there an Ezafe attached to زرد?

The Ezafe on زردِ (zard-e) serves a different purpose: showing possession rather than adding another adjective. The phrase درشت و زرد functions as a single descriptive block. Once that block is finished, the Ezafe after زرد connects the whole "large and yellow beak" to its owner, پرنده (the bird).

How exactly does the word پرنده‌شناس translate to "ornithologist"?

It is a compound noun made from پرنده (bird) and شناس (the present stem of شناختن, which means "to know" or "to recognize"). Combining a noun with a present stem is a very common Farsi pattern to create a profession or expert title, so it literally translates to "bird-knower."

Could we drop the preposition به and just use را for the object of خیره شد?

No, because the compound verb خیره شدن (to stare) is intransitive, so it cannot take a direct object with . Just like in English where you must stare something, in Farsi you must use the preposition (to/at) to introduce the thing being looked at.