Add the cranberries, jalapeno, and brown sugar to the bowl of a food processor. Cover and process until a thick paste forms.
Lay out a good-sized piece of plastic wrap. Spread the cranberry mixture into an even layer over the plastic wrap, forming a rectangle that is as long as the goat cheese and wide enough to wrap around the circumference.
Unwrap the goat cheese and place it on the cranberry mixture. Then, use the plastic wrap to form the cranberry mixture around the cheese, allowing it to stick to the cheese. Wrap any excess plastic wrap tightly around the log, and twist the ends to seal it. Store in the refrigerator until ready to serve, at least 1 hour.
Remove the cheese log from the fridge, unwrap it, and let it sit out at room temperature for 15-30 minutes or until room temperature. Serve with crackers for spreading.
Notes
One small jalapeño gives this cheese log just enough kick to add some great flavor. If you want it spicier, use two small jalapeños or one large jalapeño.