How to build a limited slip differential?
If you haven't seen it, Sariel's limited slip differential technique might do what you want, but it's a little different than what you are asking for:



This setup doesn't provide a clean way of producing a fixed amount of torque to a wheel if it's partner is running free. It instead simply disables the differential if the wheels have been running at different speeds for too long. This isn't a perfect solution, but it is very simple and may work for you depending on exactly what you are trying to accomplish.