This building was a former bakery operation (as of the early 1980s directory, listed as "Heights Bakery" though it's possible it was something originally), with a large three-point sign located at the corner that has faded off completely. As of this writing, the building is scheduled to become a wine bar/shop called "La Grande Rue" and a restaurant called "Savoir". Their websites are (also as of this writing) almost identical. According to HCAD, the build date is 1930 but Loopnet says 1950. However, the building does not seem to be on Google Earth's 1944 view but is on 1953, which suggests 1950 is perhaps the actual build date. More information can be seen on the Houston Architecture Forums.
Picture above is from May 2018 (by the author); picture below from Loopnet before renovations began.