I thought I would offer another interpretation of the image. Something of an infrared look, I suppose--I really wanted to darken the sky, and control the highlights on the surrounding rocks in order to bring out the hut. If interested, you may find a larger version here
--I think it shows some of the changes better.
Color Temp: 5500K, Tint: +4, Blacks: 9
Tone Curve: Compression 62, Luminance -37, Brightness 44, Contrast 27, Compression -65, Luminance -27
This curve brightens the mid-tones, which lowers the contrast between the highlights on the rocks and makes the light look less harsh, while maintaining the shadows.
I cropped it to get rid of the viewing platform--the only element I really wanted on the left was the shadow in the wall next to the hut--I really wanted to show the hut, rocks, sky, and clouds in the crop, and each, in a sense, has a side of this image.
I still find the image to be a little harsh, so I decide to split tone it, cooling the shadows and warming the highlights very slightly: Highlights: Hue 55, Sat 34 ; Shadows: Hue 242, Sat 25
Though I usually use Convert to Black and White Pro for conversion, and prefer it, I decided to use the Channel Mixer in Lightroom, with these settings: Red: 13, Yellow: 36, Green: 39, all others zero. All that leaves me with this:
The harshness of detail is still a little too much for me, and I want to soften both the highlights and the shadows. To do this, I duplicate the layer, apply a moderate Gaussian Blur to the new layer, and set the opacity to 10%, which is the least I can use and still notice the difference. I find that, for me, this makes it easier for my eye to look at the image. I masked out the clouds, because they did not need any additional softness.
The sky was still too light for my taste, and I wanted to do something about the rocks, so I applied a curves layer in which I pulled the shadows down (I pulled the point 1/3 of the way across the curve down to less than 1/8 of the way up--see photo). This fixed the sky, but I had to mask out the hut, to keep it bright. The change was too much for the rocks, too, so I went over all off them on the mask with a brush letting in the change at 33% opacity, being careful of the shadow line on the left, and after some fiddling, that worked out for me. Here is a photo of the settings: