Mozart and Beethoven. Western classical music is much more popular now among young Asians than among young Westerners. See for example. It's become a trendy status symbol.

If you're asking about traditional Asian music styles, the closest you'll find is traditional Chinese court music, which was exported along with other aspects of traditional Chinese culture (eg Confucian canonical texts, writing, philosophy) to surrounding nations in the Sinosphere like Korea and Japan, where it is now known as gagaku. This is nowadays nowhere near as popular in Japan as Western classical music, however, and not much listened to in China.

Arguably a better equivalent to the Western World's shared esteem for classical composers would be East Asia's common recognition of Classical Chinese poets like Li Bai and Du Fu.