In a large roasting pan, toss vegetables with oil and 1/4 tsp. each oregano, salt, and pepper. Pat chicken dry with paper towels; place on top of vegetables and sprinkle with 1/2 tsp. salt. Roast 20 minutes in a preheated 425-degree oven.
Meanwhile, in a 2-qt. saucepan, stir vinegar, sugar, espresso powder, 1/4 cup water, remaining 1/4 tsp. oregano, 1/8 tsp. salt, and 1/4 tsp. pepper. Heat to boiling on medium-high heat, stirring. Reduce heat, simmer 8 to 10 minutes or until thickened and slightly syrupy.
Brush chicken with sauce; roast 15 minutes. Brush with sauce; roast 10 minutes or until thermometer inserted into thickest part of chicken reaches 165 degrees.
Transfer chicken and vegetables to platter. Strain pan juices into measuring cup; discard fat. Pour juices over chicken and vegetables. Garnish with parsley.