After much research (because I'm so enamored with it), the most I can say is that this commercial/residential building at Váci utca 15 was designed by Majorossy Géza and Hofhauser Elek in 1900-1901. According to "Budapest in Detail" (Lőrinczi Zsuzsa, [ed.], 1999,2005): "Motifs of the Middle East reached Hungary with the mediation of Italy. This is well illustrated in the pronounced arched, framed roof gable at No. 15 Váci Street with its divided fields, in which pomegranates and tulips grow out from the characteristic Renaissance-style 'Italian pitcher,' reflecting the influence of Oriental, Turkish art."
I hope to go back in sunnier weather with a better lens and try to get a higher perspective from across the street.