You go to the reentry permit desk after the immigration officer stamps you out, pay the fee, get the permit. Open 24hrs, ask an officer if there is no staff visible at the desk.
Because you quickly learn that what one immigration officer says often differs from what the next immigration officer says and both often differ from what the actual regulations say.
This <might> be the letter from BOI approving your entry as an employee of the BOI company (I'm unsure as the English translations usually don't match up - need to compare the Thai doc names). The company would request that from the BOI Single Window site: