"a broadening" is correct and can be used in written English.
It means to make something wider or more expansive. For example: Education is the key to a broadening of opportunities for young people.
It will be a broadening of the straight format".
There's been a broadening of the national attention span.
A broadening of his palette has helped as well.
Mr. Jungen sees the Harlem work as a broadening, not abandoning, of his basic themes.
I think there's just a broadening of tastes, a broader acceptance of these tones".
"There's a broadening of people's views of what having sex means.
It's good to see a broadening in the range of genre of YA books.
Although Socialist Realism remains the dominant style, these sections reveal a broadening of subject matter.
Huckabee told me that he welcomed a broadening of the evangelical political agenda.
"In recent months we've seen a broadening of that, much more plans to attack western lifestyle.
So by all means, let's have a broadening of the imagination.
