Learn Hardcore Korean: gireul geonneol ttae josimhaeyo. - Be careful when crossing the street.

In Korean, 건너다 (“to cross”) is a transitive verb, so its object 길 (“road/street”) needs the object particle -을 (after a consonant). Hence 길을 건너다 = “to cross the street.”

What exactly does 건널 때 mean here?

건널 때 is a time clause made from the verb stem 건너- plus -ㄹ 때 (“when”). Literally, 건널 때 = “at the time of crossing” or simply “when (you) cross.”

Why is the sentence ending in -해요? Isn’t that the dictionary form 조심하다?

조심하다 is the dictionary (base) form “to be careful.” To make it a polite, present-tense sentence/advice, you conjugate it to 조심해요.

Is 조심해요 an imperative or descriptive form here?

It’s a mild imperative or suggestion. Even though it’s grammatically present tense, the intended meaning is “Be careful.” You’re advising someone.

Can you omit -을 and just say 길 건널 때 조심해요?

No. Because 건너다 takes a direct object, you must mark 길 with -을. Omitting it would sound ungrammatical.

How do I make this sentence more formal or honorific?

Switch -해요 to -하세요:
길을 건널 때 조심하세요.
This raises the politeness level to a more respectful form.

Why is there no subject like 저는 or 너는?

Korean often drops subjects when they’re obvious from context. Here it’s understood as “you” or “people in general,” so no subject is needed.