Just due to its general weirdness: might that be a Euphorbia?

I googled them and can't find any that look anything like it, but they're all so very different.

Thanks so much for your response! It's a good starting place.

Bumping to see if anyone has any more thoughts.

Have you tried pulling off a leaf? If it does not have milky sap that might help rule out Euphorbia. Not all have that characteristic but the plant in the image looks like one of those that would.

The paired, opposite blue leaves ... and then the alternate purplish leaves which could pass for azalea....

I'm tempted to call the paired blue leaves "bracts" (and/or "cyathophylls"), except that if this were a ("typical") Euphorbia, the blue bracts/cyathophylls should be growing atop the cluster of azalea-ish leaves rather than vice versa!

Euphorbia amygdaloides was the best Euphorbia match I could find for the azalea-ish leaves, including the purplish color. But I am not in any way an expert.

So, all you experts: what the heck has totally dissimilar-looking leaves like this?

katisu, if it is a Euphorbia and has milky sap, the sap might be caustic and burn your skin, so be careful!

The anatomy of Euphorbias:
http://www.euphorbiaceae.org/pages/about_euphorbia.html

I don't know how I missed your post, missingtheobvious. That is a good possibility. I've also found Euphorbia dulcis (Chameleon Purple Spurge or some such thing) could be a viable option. But I can't find a good picture of the lower half of the plants. It's like it has two different kinds of leaves, and I'm not finding that on any of them that look anything like this.

I've updated with a photo of what it now looks like. It has become my favorite plant in all of my garden.