Jo Yeo Jung stars in both and she's wild. Her characters start in a similar places, as a seemingly too good to be true housewifes having perfect lives. Both shows tackle infidelity. Both have one character approaching others with a hidden agenda and one that's an incorrigible cheater falling lower and lower, too.

Both center around a man who runs a place in a zone out of the ordinary life (an inn on the desert / midnigth eatery). Despite wuxia disguise, Ashes of Time share similar slice-of-life vibe that Shinya Shokudo is famous for, featuring several smaller stories of different people.

If you like the way Stranger is filmed, check out Awl. It's produced by the same company & I suspect it shares the same filming crew (at least to some extent). Both have very elegant, muted colour palette consistent through a whole runtime (greener in Awl, blue to light warm brown in Stranger). Music is limited mostly to background sounds and instrumentals and it's sparsely used, OSTs come mostly in ending credits, like a MV's teaser. Flashbacks are used for the sake of the storytelling, not filling the empty spaces to meet the time limit. Both are of excellent quality.
One of the main characters in both isn't very expressive and doesn't socialise much (in Stranger he's nearly emotionless due to a brain damage, in Awl it's just a way he is: gentle and rigid).
The topics are different, but hitting similar tones and both approach them with similar attitude: showing some kind of a corruption in a broad context, as a systematic, social failure based on relationships between humans. Stranger is sexier and wittier as it takes place between Prosecutor Office and Police and involves high officials and men in power, whereas Awl's more revolting (it showcases a conflict between a labour union and a mart's foreign executives), yet both have similar down-to-earth setup and problems are solved in a realistic pace.

both present the situation of an extremely capable woman in times women had little to no perspectives on getting an education and using it for the common good. They aren't greedy for power, but want it to save the state or improve the quality of ordinary people's lives. Their idealism comes in pair with an acute political sense. Even though they're surrounded by the men who love and admire them, their advice is often disregarded, their possibilities limited and their lovers would gladly just put them in a cage so they wouldn't get hurt. You got your fun, girl, now go home and let the boys play.
Both are gender-benders (short arc in Empress Ki, more in Tempest) and hide their identity. Both have multiple love interests. Both become a ruler's concubine. Empress Ki has stronger rivalry in the harem, while in Tempest even though the harem is a scene of a financial schemes, women are in comradery.

Both are about establishing great things for the common good: one about an accurate Joseon map, the other about an easy writting system. Both matters are presented as life and death and treated passionately.

Both have similar filming style and visualization techniques. Both present a group of people randomly brought together and forced to play a game with their lives at stake. Greater powers operate behind the scenes.