FILL-in is what is needed....something to "elevate" the shade exposure "upward", so that it is closer to the correct exposure for the SUN-lighted areas in the back. The easiest way to do this is to use a very LARGE reflector, or a pair of them. By large, I mean the size of a twin bed, or bigger. No, I am not kidding. "Panels" made with PVC frames fitted with tightly-stretched reflective fabric, and propped up with light stands, or "arms" have been a standard for this for decades. I say this is the easiest way because "reflector fill" is WYSIWYG....you can SEE the effect, and your in-camera light meter can measure the right exposures!!! In ***my** opinion, reflector fill usually produces superior-looking, more-natural,better lighting, for most people, under most conditions. it just looks more-natural AND the color temperature of the light reflected back usually looks very natural as long as the reflectors are white, or silver. GOLD reflectors often produce a very cheesy, warm, fakey-looking effect most of the time--but CAN be okay when you know how to use that for an advantage.
The second way, a little bit harder, is to Fill-in the shadowed ares with FLASH. aka "fill-flash".
This is NOT a neutral density filter situation.