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1
Cut the onions in half lengthwise, and then take off the ends, where the last of the peel is probably clinging a bit. Cut each half in half. Slowly, slice the onions. Try to make the slices as even in size as possible.
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2
Set a Dutch oven or large, wide pot over medium-high heat. When the air above the pot feels hot to your touch, pour in the oil. Add the butter. When the butter has melted and the oil shimmers in the pot, add the sliced onions. Toss them to coat with the oil and butter.
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3
After 10 minutes, pinch the sugar (if using) and salt over the top of the onions and stir well to coat. Cook the onions, stirring every 10 minutes or so, until they soften and then begin to reduce in volume. After about 30 minutes, the onions shrink into themselves, browning. Stir the onions, scraping the bottom of the pot with a metal spatula, to catch all that brown caramelized goodness.
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4
Don't let the onions burn! One bit of burn and the entire pot of caramelized onions will taste nasty, furrowing the brow of anyone who eats them. You don't want that.
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5
Turn down the heat to medium. Cook the onions, stirring and scraping the bottom of the pot about every 2 to 3 minutes, to make sure they don't burn. If you wish, you can add a tablespoon of water to deglaze the pot and make sure you don't miss any of the browned bits. This is where you have to be attentive.
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6
After 45 minutes, the onions will be lovely. After 60 minutes, the onions will be dark brown, wafting a slight sweetness. The longer you cook them, the darker and sweeter the onions will grow.
