The broiler setting on your oven is similar to grilling outdoors. The food is cooked by high-temperature direct heat applied to the food rather than the indirect heat of baking. Smoke is an annoying normal occurrence when broiling steaks, but excessive smoke can often be prevented by using a broiler pan and following your oven's instruction manual.
Use a broiler pan. This is important because the broiler pan was designed to allow grease to fall into the drip pan instead of into the oven. Aside from burning, grease splattering within the oven is the main cause of excessive smoke. You can line both parts of the broiler pan with aluminum foil to make cleanup easier. Remember to cut slits in the top pan's foil to allow the grease to reach the drip pan.
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Add a little water to the bottom of the broiler pan. When the fat hits a dry and hot pan, it sizzles and smokes. Adding 1/4 inch of water into the bottom of the broiler pan keeps the grease from hitting a dry pan.
Experiment with different marinades. Some oil based marinades may cause more smoke than others.
Cut excess fat from steaks before broiling them. The less fat there is on the steak, the less grease you will have popping and splattering in the oven.
Try lowering the rack in your electric oven. Thicker steaks should be farther away from the heating element than thinner cuts. This will help you avoid burning the outside of the steak while the middle is still being cooked.
Watch your meat carefully. Broiling is one of the fastest methods of cooking steaks. If you overcook the meat, smoke is unavoidable.
Clean your broiler pan after each use. Old grease will smoke as it burns away.
Close the oven door if you are using a gas oven. Gas ovens are meant to have the door closed during broiling. The door of an electric oven should be left slightly ajar. Leaving the door slightly open while broiling in an electric oven allows steam to vent and prevents the oven from getting too hot.