"broad outlines of" is correct and usable in written English.
You can use it to refer to a general description or overview of a topic. For example, "The report provided the broad outlines of the plan."
The broad outlines of what happened next are well known.
They say they've got the broad outlines of a deal.
But the broad outlines of what lies ahead are clear.
The broad outlines of the budget are as follows.
The broad outlines of two proposals began to take shape.
Congressional leaders continued to work on the broad outlines of a rescue plan.
McCarthy focused on two main points as she went over the broad outlines of the plan.
Still, Mr. Serrano and others acknowledge the broad outlines of the problem.
During the presidential campaign Mr. Bush sketched out the broad outlines of his foreign policy thinking.
With his speech, Mr. McCain laid out the broad outlines of his general election campaign.
City and state officials described the broad outlines of the agreement.
