Adjust oven rack to middle position and heat oven to 400°F.
Make the paste/marinade by pulsing 1/3 cup pitted green olives, 1/3 cup pitted prunes, 1/4 cup extra-virgin olive oil, 4 garlic cloves, 2 tablespoons capers, 1 teaspoon dried oregano, ½ teaspoon pepper, ½ teaspoon kosher salt and ¼ cup white wine in food processor about 1 to 2 minutes. Transfer to bowl. (Paste can be refrigerated for up to 24 hours.)
Use the paste to marinate the chicken, by coating it completely in the paste mixture.
Place chicken on a rimmed sheet pan. Pour white wine and chicken stock onto the sheet pan, sprinkle the 1 tablespoon of capers, ⅓ cup olives halved and ⅓ cup chopped prunes around the chicken. Sprinkle the dish with brown sugar and salt.
Bake in the oven for 30 minutes. If you would like the meat and veggies to have a bit of char, broil for 3 minutes or until desired caramelization is achieved.
Remove the chicken onto a serving dish along with the olives and prunes. Pour the warm pan drippings into a small saucepan, bring to a simmer and reduce by half. Whisk in cold butter until fully incorporated.
