You're correct that a "reflector board", even the soft side throws a very strong and harsh light. If this is the only equipment you have available, then back if off so that it's not as painful. Depending on the size of the shot you can shoot it through a silk or grid cloth too.
There are however other means of reflecting a large quantity of softer light, such as with the use of a 8x8' or 12x12' Ultra Grid, Grifflin or even a Muslin. Of course this type of equipment presumes that you have the staffing to build and control it in windy conditions. You can use large tent spikes and rope, or tie it to a tree or a vehicle so that is stays still.
Make sure your production insurance is up to date with the use of any of the above.
The principle at play here is that the larger the size of the light source the more soft it can be and still deliver the quantity of photons necessary to balance the open lighting in the background. Furthermore, remember that it's completely natural for the subject in the shade to "be in the shade". You probably don't want them to be silhouetted however, so find the happy medium.
Finally your choice of camera and gamma setting will have a large part to play. If all you have is a DSLR with limited dynamic range you'll have to do more with the lighting. If you have an Alexa of Sony F5/55 your camera will be able to hold the highlights and still reach into the shadows.
John has the answer. I'd only add that there is a "reverse" way to look at the situation; instead of lighting the talent, dim the background down so it's closer to the level of the foreground, using a neutral density gel in indoors near windows, or when outside, a black mesh cloth.
If the camera and lens are set up right, they won't read the mesh as being there at all, but if you get it wrong, you might see Moire'.