Tourist visa L - Multi Entries for 6 Months / 12 Months (South Korean)

Yes, it's possible. Besides flight and hotel booking confirmation, you need to provide your passport, application form, recently-taken photo, and residence permit in HK.

Generally HK temporary residents will be granted multi-entry visas only after receiving two tourist visas issued in HK in the past. The maximum validity is usually no longer than 12 months. Permanent residents can in addition "graduate" to holding a three-year visa after receiving a 12-month visa. Nationals from certain countries (US, Canada, Brazil, Israel and Argentina) are already eligible for 5 or 10-year visas but the criteria for issuance in HK can vary.