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Cook's Note: A skin-on chicken breast with wing bone attached and wing tip and tenderloin removed is also known as an airline chicken breast.
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Preheat the oven to 250 degrees F.
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Pat the chicken breasts dry with a paper towel.
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Coat a medium saute pan with olive oil, and place over medium-high heat.
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When the pan is hot, sprinkle the skin of the chicken generously with salt, and then place skin-side down into the pan.
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Cook until the skin is golden and crispy, 4 to 6 minutes.
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Sprinkle the opposite side of the breast with salt, and then flip the chicken and continue cooking until cooked through, another 5 to 6 minutes.
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If the pan starts to smoke, lower the heat.
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Transfer the breast to a sheet pan, tent loosely with foil and place in the oven until the sauce is finished and you are ready to plate.
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Remove the excess oil from the pan before returning over medium-high heat.
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Add the clementine juice, clementine supremes and vinegar, scraping up the brown bits that cling to the bottom of the pan.
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Stir in the thyme and chiles and let the liquid reduce by half before pouring in the chicken stock and a pinch salt.
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Continue cooking until the stock has reduced.
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Taste the sauce, making sure it's delicious, and then remove the thyme stalk and season with more salt, if needed.
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The sauce should be thickened and a little chunky.
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Lay the Yukon Gold and Cauliflower puree on the bottom of the plate, and then slice the chicken breast and fan the slices on top.
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Spoon some of the sauce on and around the chicken, and garnish with the supreme clementines.
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Halve the potatoes, and then cut each half into 6 to 8 pieces.
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Place the potatoes in a pot large enough to hold the cauliflower as well, and then cover the potatoes by 2 inches of water.
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Sprinkle generously with salt (it should taste like the ocean) and bring to a boil.
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After the water has been boiling about 10 minutes, add the cauliflower and cook until the vegetables are fork-tender.
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Bring the cream to a scald in a small saucepan.
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Meanwhile, pass the potatoes and cauliflower through a food mill into a large bowl.
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Add about half of the hot cream and 1/2 of the butter, and stir with purpose until thoroughly combined.
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Repeat this process with the remaining cream and butter until incorporated.
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Taste for seasoning (you will probably have to add salt), and serve warm.
