"broad understanding of" is correct and usable in written English.
It can be used to describe a wide-ranging knowledge of a particular topic. For example, "He has a broad understanding of international politics."
Having a broad understanding of this history has helped me quickly see the significance of Nash's contribution.
Obama encouraged Howard graduates to "be confident in [their] blackness" and to embrace a broad understanding of racial authenticity.
Only in Britain is a broad understanding of your nation's past regarded as anti-European, if not downright racist.
From the beginning, Peekskill, a city of about 24,400, had a broad understanding of the term artist.
That workers take on multiple roles also means that they have a broad understanding of the business, he adds.
It contributed nothing to a broad understanding of the two religions by either their respective practitioners or interested observers.
I would hope it's someone who has a broad understanding of public lands and isn't just energy, energy, energy.
Unfortunately, economists do not have such a broad understanding of the natural world in which they operate.
But in what appears to be the first admission to the contrary, Blears said: "The committee did have a broad understanding of what the capabilities of GCHQ were".
Gaps in the science: what we don't know But like all science-based goal setting, tying one's sustainability strategy to a broad understanding of ecosystem services is complicated.
"Since graduating I have passed my IEMA associate entry exam which enabled me to demonstrate a broad understanding of environmental management.
