Which of the following sentences requires a question mark?: How do you want me to make the omelet We are out of eggs
How do you want me to make the omelet?
You can use a question mark after omelet. It will make a simple sentence.
Well, it is not all. If you like to add the second clause including it, you can do it easily.
How do you want me to make the omelet where we are out of eggs?
This is a complex sentence now but it has another name that is called "embedded question". It does mean one question is added with another question but the second clause needs not to use an auxiliary verb before the second subject.