Preheat the oven to 375°F.
Place a medium-size ovenproof sauté pan over medium heat and add 1 tablespoon of the olive oil. Season the thighs all over with kosher salt and black pepper. Add the thighs to the oil, skin side down. Make sure there is space between them and that the heat is not too high. Slowly crisp and render the chicken skin, cooking it for about 15 minutes. Remember not to touch the thighs; just let the skin crisp and the fat render.
While the chicken is crisping, start the risotto: Combine 1 cup of water and the chicken stock in a small pot and set the pot on a back burner on low heat. Take a heavy 3-quart pot, place it over medium heat, and add 1 tablespoon of the olive oil. When the oil is hot, add the onion and cook for 3 minutes, until softened. Add the barley, stir and toast for 1 minute, and then slowly add about 1 cup of the stock mixture. Cook, stirring often with a wooden spoon, until the barley begins to look a little dry; then add more stock. Repeat, gradually adding the remaining stock mixture. Risotto likes moisture but doesn't want to be drowned.
When the chicken skin is very crisp, turn the thighs over and place the pan in the oven. Roast for about 10 minutes, until cooked through.
In a large cast-iron skillet, add the remaining 1 tablespoon of the olive oil and place over high heat until it comes to a slight smoke. Working in batches if needed, add the zucchini rounds and char until they blister, but still have a firm bite, about 1 or 2 minutes per side. Set aside on a paper towel-lined plate.
Back to the risotto. Slowly but surely you will have cooked the stock into the barley. After about 20 or 25 minutes you will be just about finished. The barley should be tender but still a touch toothsome at this point. Season with kosher salt to taste, and add the butter and cheese and stir well. Gently fold in the zucchini rounds, partially cover, and set aside on the stovetop, but removed from the heat, to keep warm.
Remove the chicken from the oven and let it rest for about 5 minutes.
Arrange the barley risotto on a small platter and top it with the chicken thighs. Eat!