All American bar @ The Avenue advertises 'stuffed' handmade burgers. You can select 3 of your own ingredients from a long list, or have one of their pre-selected menu. Haven't tried it yet, will get pics and review if I do.
Pastrami on Rye (Jomtien 2nd Road and Theppisit) has burgers. Haven't had one of those either, but their sandwiches and deep dish pizza are recommended.
Edited by kathoeyfan, 11 June 2016 - 10:29 PM.