How can I settle a minor personal injury claim against me out-of-court for cash? I ran over a woman's foot while driving uninsured. Thank you.

Has she filed a lawsuit? If so, most courts will require that the parties "mediate" with a third party mediator to see if they can resolve it out of court. If it has not been filed in court yet, you can contact her and see what she wants and negotiate from there. You will want her to sign a release, if you reach a settlement, in exchange for the check.  IF her insurance company compensated her, they may be entittled to repayment as well, so consider that. It is likely best to hire a lawyer to work through this with you to make sure it is done correctly.