Learn Hardcore Korean: sikdangeseo menyureul goreugo isseoyo. - I am choosing from the menu at the restaurant.

식당 means “restaurant.” The particle -에서 marks the place where an action happens (“at / in”). If you used 식당에, it could mean “to the restaurant” (destination) or “exist at the restaurant,” but it wouldn’t clearly say “I’m doing something there.”

Why is there no subject (like “I” or “we”) in 식당에서 메뉴를 고르고 있어요?

Korean often omits the subject when it’s clear from context. Here, because you’re talking about what you’re doing right now, the subject is implicitly “I”. If you wanted to be explicit, you could say 저는 식당에서 메뉴를 고르고 있어요 (“I’m choosing the menu at the restaurant”).

What role does 를 play in 메뉴를 고르고 있어요?

를 is the object-marking particle. It tells you that 메뉴 (“menu”) is the direct object of 고르다 (“to choose”). Without 를, the sentence can sound vague or overly casual.

Why is the verb phrase 고르고 있어요 used instead of something like 골라요 or 고릅니다?

고르고 있어요 is the -고 있다 construction, which expresses an ongoing action—“am choosing.”

골라요 is simple present (“choose” as a habitual or general fact).
고릅니다 is the formal-polite simple present (“I choose”).
If you want to say “I am choosing right now,” you need -고 있어요 in casual-polite speech.

How does the progressive -고 있다 construction work in Korean?

Attach -고 to the verb stem (고르 + 고) and follow with a form of 있다. It literally means “be in the state of doing X.”
Structure:
[Verb stem] + 고 있다
Casual-polite: 고 있어요
Formal-polite: 고 있습니다
This is equivalent to English “be …-ing.”

How do I know that 있어요 here is part of the progressive rather than the existential verb (“there is”)?

Context and form tell you: when 있다 follows -고, it’s the progressive marker. If 있다 comes right after a noun plus 에 (like 식당에 사람이 있어요 “There are people at the restaurant”), it’s the existential “there is/are.”

Can I drop the object particle 를 in casual conversation and just say 메뉴 고르고 있어요?

Yes—native speakers often drop particles in fast, casual speech: 메뉴 고르고 있어요 is perfectly understandable. However, in writing or more formal contexts, it’s better to include 를 for clarity.

What about saying 메뉴판 instead of 메뉴? Are they interchangeable?

메뉴 (loanword from English) refers to the list of dishes, just like “menu.”
메뉴판 adds 판 (“board”/“card”) and often emphasizes the physical menu card/book.
In most cases you can use them interchangeably when you’re choosing what to eat.

Is there any difference between 고르다 and 선택하다, since both can mean “to choose”?

Subtle nuance:

고르다 is more “to pick out” or “to select from a group” (more casual, common in daily use).
선택하다 is more “to make a decision/selection” (slightly more formal or abstract).
In the context of picking a dish at a restaurant, 메뉴를 고르다 sounds the most natural.