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Lay chicken pieces snugly in a Dutch oven. Drizzle with olive oil and season liberally with salt and pepper. Place in the oven and roast, uncovered, checking every 15 minutes to see if juices run clear when the thickest part of the thigh is poked with a paring knife. Remove the pan from the oven when chicken is done.
Heat the vegetable oil in a large saute pan over medium heat. Add the shallots and cook, stirring, until soft but not browned, about 3 minutes. Remove the pan from the heat and add the wine. Carefully return the pan to the heat, adjust the heat and simmer until the wine is reduced by half, 15 to 20 minutes. Add the carrots and capers. Cook on low for 5 minutes. Add the potatoes, broccoli and stock. Simmer until the broccoli is just barely tender and the potatoes are heated through, about 3 minutes. Add the vinegar, parsley and butter. Gently stir until the butter has melted. Add salt and pepper to taste.
On a serving platter, arrange potatoes on bottom. Place the cooked chicken on top. Spoon remaining vegetables and pan sauce over everything. Garnish with more parsley and serve with bread or rolls.