@misterlisty I don't quite see how 35 KB is a "large file"... There must be something wrong in your setup, it is common to upload much larger files than that to perform OTA firmware upgrades for instance.
Can you give more details about the setup, including whether the module is acting as a station or AP, what you have between the client and the device, any logs shown on either side, what type of file you are uploading...
Tcpdump or wireshark captures could potentially be interesting as well.