This is not a dynamic range issue. You're trying to match a visual function called Color Constancy. That always requires some manipulation...either of the scene lighting or in post processing.
Here is an example of Color Constancy...
The squares labeled A and B are both the same shade of gray...they're both RGB 120, 120, 120. Your visual system is being fooled into brightening the B square by the cylinder's shadow. To draw an analogy, it's like raising ISO on specific areas of the scene to make them brighter than others. Your visual system tries to show you what it thinks it's looking at. Your brain performs this function to assist you in identifying objects...potentially dangerous objects...such as poisonous snakes slithering in the shadows under trees.
The Color Constancy function is triggered by large differences in lighting, such as the 3-4 stops difference between sunlit plains and the shaded area under a large tree. So when you have two clear light sources in the image (such as the sunlit areas and areas of shade lit by the sky glow) you'll likely have this issue. Some images, like the CheckerShadow illusion, can trigger the function. However, most shots of high contrast scenes do not. What you see in your image is the actual difference in lighting that your visual system was keeping from you.
What you want is the nice, 1 EV difference in luminance that your eyes had shown you...not the 3-4 EV difference that's actually there (or more, in the case of a bright window and dark room.) Once you understand what's going on, you can now take steps to address the issue. One method is to use a graduated neutral density filter to balance the scene. With some scenes you can use flash to balance the lighting. If you have some highlight range DR, you can overexpose (ETTR) and use that extra DR to fix the image in post processing. HDR processing of multiple images works for static scenes. Still another solution is to reframe to eliminate the shadow or the shade.
But know this...there is no camera, nor any exposure setting, that will give you the scene as you see it. That's impossible. That said, camera makers are trying...with functions such as Nikon's Active Dynamic Lighting. But that's still a long way off from doing what your visual system can do.