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Step 1
Let the chicken thighs sit at room temperature for at least 15 minutes. Heat a 12” cast-iron skillet over medium heat. Add enough olive oil to coat the bottom. Season the chicken well with salt and freshly cracked black pepper.
Step 2
When the oil is hot, place the chicken skin-side down into the skillet. Cook for about 5 minutes. Lower the heat to medium-low and continue to cook until the skin is golden and crisp, about 3 minutes longer. Flip the chicken and cook for another 5 minutes, or until cooked through. Transfer the chicken to a plate.
Step 3
Add the sliced butternut squash to the skillet over medium heat. Cook for about 8 minutes until caramelized, stirring & flipping the squash slices often so they don’t burn. Reduce the heat to medium-low and cook for about 5 more minutes. Add a 1/4 cup of water, cover the skillet with a lid, and cook for another 5 minutes or so until tender. Season well and transfer to a plate.
Step 4
Raise the heat to medium. Drizzle in a little more olive oil. Add the swiss chard and apple cider vinegar. Quickly saute for about a minute. Season well and transfer the greens to the plate of squash. Cover with foil to keep warm.
Step 5
Add the butter and chili peppers to the skillet. Allow the butter to melt and slightly brown as the peppers cook. Stir in the mustard, maple syrup, and remaining 2 tablespoons of apple cider vinegar. Bring the sauce to a simmer, reduce the heat to low, and add the chicken back to the skillet, skin-side up. Simmer for 5 minutes to reduce the sauce and warm the chicken.
Step 6
Meanwhile, make the polenta. Add the water, thyme and a pinch of salt to a 2qt saucepan. Bring to a boil. Whisk in the polenta. Reduce the heat to low and cook for about 5 minutes, or until the polenta is tender, stirring often. Remove the thyme. Stir in the cheddar and butter until melted.
Step 7
Spoon the polenta onto a large platter. Arrange the squash, greens, and chicken over the polenta. Spoon all the remaining sauce over top. Garnish with any extra thyme leaves and more freshly cracked black pepper.