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Divide ground chuck into 6 sections and shape into patties. Heat 1 teaspoon of olive oil over medium heat (you could do it on the grill instead!); add 3 patties and cook about 5 minutes on each side or until done. Repeat with another teaspoon of olive oil and the rest of the patties. Once cooked, remove from heat and add a slice of cheese on top.
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While your burgers are cooking, add a teaspoon of olive oil to another pan and heat over low heat. Add sliced green peppers and onions and cook, stirring often, until the veggies have softened.
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Assemble your burgers before cooking the eggs: put a cheese-covered patty on each bun, add a slice (two halves) of bacon, and a pile of cooked veggies.
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Heat the final teaspoon of olive oil over medium heat. Add the eggs, a few at a time, and cooked until the whites are cooked and the yellows are still gooey. Put an egg on top of each burger. Serve hot with salsa on the side to put on top.