Learn Farsi: آنچه از این تجربه یاد می‌گیریم، حکمت گران‌بهایی است. - What we learn from this experience is a precious piece of wisdom.

آنچه means that which or what in a declarative sense, making it perfect for this pseudo-cleft structure. You cannot use چه because it is strictly a question word. While چیزی که (the thing that) is very common in everyday speech, آنچه gives the sentence a slightly more formal, thoughtful focus, which perfectly fits a statement about wisdom.

Is it also correct to say آنچه که in this sentence?

Yes, آنچه که is entirely correct and means the exact same thing. The که is technically redundant but very common, especially in spoken Farsi, because it helps the rhythm of the sentence. Leaving it out, as done here, makes the sentence slightly more concise and literary.

Why is there a یی suffix on the end of گران‌بهایی?

This is the indefinite ی suffix, which acts like the English article a or an. Because گران‌بها ends in the long vowel sound a (alef), we need the glide consonant ی before adding the suffix, resulting in یی. Therefore, حکمت گران‌بهایی translates to a precious piece of wisdom.

How does the compound adjective گران‌بها break down?

It is formed by combining گران (heavy or expensive) and بها (price or value). Together, they form an adjective meaning highly valuable or precious.