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1
Make the Peppers: Heat the oil in a very large pot. Add the peppers, and allow to sweat for 2 to 3 minutes. Add jalapenos, and salt to taste. Cook over medium-high heat for about 20 minutes, or until the peppers have softened and are partially tender. There will still be some liquid left in the pot. Add the tomatoes and the basil leaves. Lower the heat and continue to cook for about 30 minutes, until the peppers are tender. Add additional salt, if needed. Remove from the heat. If canning, add the vinegar, place in canning jars, and process according to the manufacturer's instructions. Or, store in the refrigerator for up to 4 days.
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2
Make the Hash: Preheat the oven to 375u00b0F.
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3
Bring a pot of well-salted water to a boil. Add the potatoes and boil until about three-quarters done, about 4 minutes. Drain well.
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4
Heat a large ovenproof skillet over high heat. When hot, add the olive oil, then add the potatoes. Lower the heat to medium and cook, tossing occasionally, until the potatoes are crusty and browned, 10 to 12 minutes. Add the onion, season with salt and pepper, and cook until the onion browns lightly, about 2 minutes. Drain the potatoes and onion in a sieve to remove the excess oil, then return them to the skillet.
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5
Off the heat, gently stir in the Damn Hot Peppers. If you blend them in too well, the potatoes will lose their crispness. Make 4 evenly spaced wells in the hash and break an egg into each well. Sprinkle the eggs with the oregano and scatter the cheese over the hash.
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6
Transfer the skillet to the oven and bake until the eggs are cooked to your taste, about 6 minutes for firm whites and soft yolks. Serve immediately.
