Preheat oven to 375°F. Coat an 8-inch square baking dish with nonstick cooking spray.
Combine cornmeal, flour, baking powder and 2 teaspoons salt in a large bowl and mix well. Whisk together egg, milk and 1 1/2 tablespoon oil in another large bowl; add to the dry ingredients and stir just until evenly moistened. Turn the batter into the prepared baking dish and bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean. Let cool in the pan on a rack. Cut into 1-inch cubes.
Heat the remaining 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add onions and celery and cook, stirring often, until softened, about 5 minutes. Transfer to a large bowl and add the cubed corn bread and parsley; toss to mix. Slowly add broth, tossing until the corn bread is well moistened. Season with salt and pepper.