Snowfall

The male main character is Gao Wei Guang
The main characters are both immortal beings
Both have the theme of eternal love

Both dramas have immortal male lead who had basically lost his meaning of life until a young strong-willed female lead appears in his life and changes everything.

If you are into a vampire story during Republican era…
Same plot device of fragile young woman who is the redemption of older blase male vampire .

Park Ji Sang is a doctor specializing in hepato-pancreato-biliary surgery in the best cancer research hospital in the country. He is also a vampire. Despite seeming cold and unfeeling, Ji Sang masks his soft heart and inner pain and yearns for closeness with people. He believes very strongly in the sanctity of human life and suppresses his thirst for blood to treat terminally ill patients and save lives. Among his colleagues is Yoo Ri Ta, a hotshot physician who entered medical school at the age of 17 and is also the niece of the chaebol group chairman who owns the hospital. Ri Ta is highly capable but snooty and prideful, yet Ji Sang finds himself falling for her. He also gets drawn into a conflict between good and evil as he encounters Lee Jae Wook, a two-faced hospital chief who gains everyone's trust with his gentle demeanor, but inwardly harbors a dangerous ambition for power and a talent for cruelty.

Both are historical dramas in which the ML is turned into a vampire and later on meets the human FL.

Both MLs are formally humans who were turned into monsters against their will, searching for the one who turned them a century or more later. Both FLs have very difficult lives but are strong characters. Both dramas have beautiful cinematography and feel like a dark fairytale.

The female leads of both shows are humans. While the male leads are vampires (well, Heartbeat's male lead is specifically half human half vampire)