Before this section became the Loop 1 / Mopac Expwy toll road that opened in 2006, it was FM 1325 which was also known as Burnet Road.  Some maps and street signs will still call it that.
Burnet Road up until 2003 didn't have a divided median and you could take a left turn from where Garbo's is (Sea Island Shrimp House at the time) to go south onto Burnet Road where the North end of Mopac Expwy begins and pass under Parmer Lane.