Found the solution:
I had to delete the engine cache in two places, the first was located in the hidden folder under Appdata → Local → Unreal Engine, I deleted that whole folder but kept the other UE4 folders there. Then the second cache was located under the project folders itself and they were the “Saved” and “Intermediate” folders. I didn’t touch the config folder since I didn’t want to re-map my inputs.
After this I started the engine back up, this re-creates the App-data folders and the engine reverts to opening like the first time (tutorial icons, UI is reset, etc). I was able to open my project which re-creates the two folders named above and tried cooking the project.
This resulted in a successful cook without any warnings.