Making up hamburger patties from fresh beef isn't the most challenging of kitchen tasks, but it does take a modest amount of time and attention. It also means a degree of organization, because ground beef is highly perishable and should be made into patties within the first day or two. Frozen burger patties offer a convenient solution to both the time and freshness problems. They're usually meant to cook from frozen, in a pan, on the grill or under your broiler.
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Your oven's broiler works rather like a barbecue grill, except the heat comes from above rather than below. Conventional roasting or baking uses the oven's elements to heat air in the oven, but broiling places the meat directly beneath the element. There, it's the infrared radiation created by the hot broiler element that provides most of the cooking. This means that your patties will brown very quickly on the surface facing the broiler, quickly developing a rich, savory flavor.
The issue with broiling meats in general, and frozen patties in particular, is that the broiler can cook the surface of the meat to a cinder before the middle is even thawed. That's because heat is very slow to move from the surface of the burger to the frozen beef inside. On a grill it's easier to judge how your patties are progressing, because you can prod the burger with a finger or your tongs and track the texture as it changes. With your broiler, you'll have to rely on one of two techniques to compensate for the difference between internal cooking and external browning.
One method for cooking better burgers under the broiler is to vary the distance between the patties and the broiler element. Most home ovens offer the option of positioning your upper rack either 4 inches or 6 inches from the element. The 4-inch distance is suitable for fresh patties as long as they're not too thick, but it's too close for frozen patties. Lower the rack to the 6-inch setting, which slows browning long enough for the patties to cook. Depending on the size and thickness of your patties, they might take 12 to 20 minutes of broiling time. Turn them at the mid-point for even cooking and browning, but be careful when opening the hot oven.
If you have a little more time on your hands, you can use a two-stage technique for your burgers. Preheat your broiler with the rack at the 4-inch position, and insert your pan of burgers. Broil them for four to six minutes on each side until they're well browned, then move them to a middle rack and reduce your oven to 375 degrees F. Cook your patties at the lower temperature for approximately 20 to 25 more minutes, depending on their thickness.
Commercial brands of frozen hamburgers are prepared under rigorous food safety standards, but should still be handled with caution. The juices should run clear when your patties are fully cooked, and they should reach an internal temperature of 160 F when tested with a meat thermometer or instant-read thermometer.