Peel the oranges, paring away all the exterior white pulp. Cut each orange into wedges. Cut each wedge into 1-inch pieces. Set aside.
Place the cayenne, paprika, garlic, olive oil and vinegar in a salad bowl. Add salt and pepper to taste and whisk to combine. Add the oranges, parsley and olives. Toss gently to blend. Serve cold or at room temperature.
