pet project
compound.a plan or activity that you care about very much and work on because you personally enjoy it.
compound.a project, activity, or goal that is pursued as a personal favourite rather than out of necessity or professional obligation. It often implies the individual has a particular emotional investment in its success.
“The community garden is the mayor's pet project.”
“While the company focuses on software, the CEO spends his weekends on a pet project involving vintage car restoration.”
“The senator's pet project, a niche environmental bill, faced significant opposition from colleagues who viewed it as a personal indulgence.”
usually used with a possessive (my, his, the director's) to show who is personally invested in the work.
explain that 'pet' here acts as an adjective meaning 'favourite' or 'special', similar to how a 'pet peeve' is a specific personal dislike.