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1
In a large heavy pot over medium-low heat, melt the duck fat (or heat the oil) and add the onions.
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2
Reduce heat to very low and cook slowly cook, stirring occasionally, until onions are a very dark brown, 1 1/2 to 2 hours.
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3
If necessary, toward the end of cooking, raise heat to medium and stir constantly until onions are browned.
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4
Meanwhile, place the red peppers in a steamer over boiling water and steam until very soft, 15 to 20 minutes.
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5
Transfer peppers to a food mill or blender and puree (straining afterward if using a blender).
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6
You should have 3/4 cup puree; reserve any remainder for another use.
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7
Add the tomato paste to the onions and cook until paste darkens, about 5 minutes.
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8
Add the sweet and hot paprikas and mix well.
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9
Add 7 cups water, the vinegar, dried marjoram, garlic, ground caraway seeds and lemon zest.
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10
Add half of each of the fresh marjoram, thyme and rosemary.
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11
Season the beef cheeks generously with salt and pepper and add them to the pot.
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12
Bring liquid to a bare simmer and cook partly covered, stirring only 3 or 4 times, for at least 3 hours, then add the rest of the fresh herbs and begin to check the cheeks tenderness with a fork.
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13
They are done when they fall easily from the fork, after about 4 hours.
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14
They should be meltingly tender, but not fall apart.
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15
As some pieces will take longer than others, pull them from the liquid as they are done.
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16
Spread the cooked beef cheeks in a single layer on a baking sheet.
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17
When all the cheeks are done, pass the cooking liquid through a colander.
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18
(Dont use a sieve, as you want to push tiny bits of onion through to make a slightly chunky sauce.)
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19
Pour the sauce over the cheeks and season to taste with salt, pepper, additional fresh marjoram and cornichon juice.
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20
Serve immediately, very hot, or reheat by covering baking sheet and returning cheeks to oven at 350 degrees.
