De or het broeiing?

The correct Dutch article is:

de broeiing

Rule Words ending in -ing: almost always de. See the rule
Meaning (Dutch) het broeien

How to use broeiing

the broeiingde broeiing
this broeiingdeze broeiing
that broeiingdie broeiing
our broeiingonze broeiing
your broeiingjouw broeiing
every broeiingelke broeiing
which broeiing?welke broeiing?
a big broeiing / the big broeiingeen grote broeiing, de grote broeiing

Dutch words ending in broeiing

uitbroeiing

In compound words, the last part decides the article. See the rule

Meaning, plural, diminutive, pronunciation and translations: WikiWoordenboek (Dutch Wiktionary) (CC BY-SA 4.0). Example sentences: Tatoeba (CC BY 2.0 FR).