Itazura Neko no Memento

With his renowned-novelist dad away from home and his mom busy with her own job, Wataru's parents hires a young male housekeeper named Osaka to help around the house. From the moment they meet, Wataru considers Osaka's relentless efforts to be part of his life a nuisance. That is, until he receives a letter that helps him start opening up. The anonymous letters Osaka continues to bring him are sweet and caring—but Wataru believes they're from Osaka himself. Wataru decides to confront Osaka directly.

(Source: Renta!)