Preheat broiler. In a small heavy saucepan, bring port wine to a boil and cook for 1 minute. Add vinegar, chicken broth, sugar, half of the figs, and the cinnamon stick. Cook on high heat until reduced by half. Simmer over low heat for 4 minutes.

Remove cinnamon stick and transfer sauce to a blender. Use extreme caution. Remove the center portion from the blender lid and cover blender with the lid and a kitchen towel. Hold them down firmly as you purée the sauce.

Gently season halibut filets with salt and pepper. Spray broiler pan and both sides of fish with canola oil or olive oil spray. Broil for 3 minutes on each side.

While fish is cooking, add sauce back to saucepan along with the rest of the fig pieces. Return sauce to a boil. Brush a little of the sauce on the tops of the fish for the last minute of broiling. Put the fish on individual plates and top with the hot sauce.