Other movies with a similar combination of sound and images

There are already a couple of Tarvovksy films in this list, but really, if you appreciate Kieslowski and in particular the depth of character and visual+sound approach to artistic film, you would do well to investigate all of Tarkovksy's catalogue. The man was a supernatural genius when it comes to film. Sadly, also like Kieslowski, he died far too young. But I agree, Zerkalo is a definite must see. When someone can put a sledgehammer to your heart with a simple image of wind blowing through billowing grass, you know you are being educated by a master.

Antonioni's Red Desert. You'd probably like it if you like Kieslowski and Tarkovsky.

I'm surprised that no one has mentioned any Asian film. Kieslowski's work is so acclaimed because, among other things, it takes a non-western approach to achieving what the OP describes. Ki-Duk Kim is a misanthrope with little concern for the rights of animals in his films. With that caveat, his "Spring, Summer, Autumn, Winter...and Spring Again" is very much like "Blue."

Caveat: animal suffering made me stop with Kim's canon after three films.

Also--"Uncle Boonmee Who Can Recall His Past Lives." Unforgettable, because it basically takes the viewer into the peace, the craziness, and the final acceptance, of death in the same way "Blue" takes one into the peace, the craziness, and the final acceptance of grief.