Marinate the apricots: In a large bowl, stir the apricots, sugar, and vinegar together. Let sit while you brown the chicken in the next step.

Brown the chicken in butter and olive oil: In a large sauté pan over medium-high heat, heat 1 tablespoon of butter and 2 tablespoons of the olive oil until hot. Working in batches to keep from crowding the pan, brown the chicken pieces on each side. As the chicken cooks, sprinkle with salt. Once the chicken is browned, remove the pieces from the pan to a bowl and set aside.

Saute the onions: Add the remaining 1 tablespoon of oil to the pan and sauté the onion until it begins to brown. As the onion cooks and releases moisture, use a flat-edged spatula or wooden spoon to scrape off the browned bits from the chicken (called fond) from the bottom of the pan. If the pan becomes dry, add water, a tablespoon at a time to help release the onion from the bottom of the pan.

Add the chicken stock: Once the onion has browned a bit, add the chicken stock and lower the heat to medium.

Purée the apricots: Set aside 1 ⅔ cups of the apricots for the finished dish. In a blender, puree the remaining apricots, along with any juice they have released. Pour the purée into the pan with the stock and onion.

Simmer the sauce: Stir the cinnamon, rosemary, and Tabasco into the sauce. Bring the sauce to a simmer. Then, lower the heat and gently simmer for 10 to 20 minutes, or until the sauce thickens slightly. Taste and add black pepper to taste. Taste again and add more salt and Tabasco, if needed.

Finish the dish: Just before serving, add the chicken and the reserved apricot pieces to the pan. Simmer gently for 5 minutes, or until the sauce is hot and the chicken is cooked through. Sprinkle with chopped parsley and serve with rice or egg noodles.