For the salad:
Preheat the oven to 400°. Lightly grease a 9 by 9-inch baking pan.
Prepare the cornbread mixes according to package directions. Pour the combined batter into the prepared pan. Bake according to the directions on the box or until a wooden pick inserted in center comes out clean. Cool completely. Invert the cornbread onto a cutting board. Cut the cornbread into 1/2-inch cubes and arrange them in a single layer on a rimmed baking sheet. Drizzle with melted butter, tossing gently to coat. Bake, stirring every 10 minutes, until the cornbread is toasted, about 20 to 25 minutes. Set aside to cool.
Preheat the grill to medium-high heat.
Combine the onion, peppers, squash, and zucchini in a large bowl. Add the olive oil and toss gently to coat. Season with salt and pepper, to taste. Arrange the onion slices on the preheated grill, cover with the grill lid, and cook for 3 minutes per side. Remove the onions from the grill, chop and set aside. Arrange the pepper wedges on the grill, cover with the grill lid, and cook for 8 minutes per side. Chop the peppers, and set aside. Arrange the squash and zucchini on the grill, cover with the grill lid, and cook for 2 minutes per side. Chop the squash, and set aside.
In a large bowl, combine all the chopped vegetables, tomatoes, and cornbread squares, Add the Lemon Vinaigrette and toss gently to coat. Garnish with chopped fresh parsley leaves and serve immediately.
For the lemon vinaigrette:
In a small bowl, whisk together lemon juice, parsley, mustard, mayonnaise, pepper, and salt. Gradually whisk in the oil until combined. Cover and chill until ready to use.