Door on my kitchen wall. What is it?

I live in a super old building. I've always wondered about two things in my kitchen that had been there since I moved in. The first was a small craved box kinda thing. It had a closing which over the years just fell off and broke. The super eventually told me it was used for storage. Extensive research from my part showed it was called an "ice box" use to store milk,cheese etc. during the milkman's era. But the second thing i was always wondering about was never answered. There's a door in the middle of my kitchen wall across from the window about the size of a small side table. It has been locked, and painted over. It is impossible to open trust me i've tired. If it is any help i know my building was built in 1928. If anyone knows anything about it or has something similar in their own apartments please share. ;)