Put the onion, yellow squash and zucchini on a baking sheet. Put the carrots, parsnips and butternut squash on another baking sheet. Season the vegetables with salt and pepper and drizzle with some olive oil. Toss to coat and spread out into a single layer.
Roast the vegetables until tender and brown around the edges, 25 to 30 minutes for the onion pan and 40 to 45 minutes for the carrot pan. Remove from the oven and let cool.
Meanwhile, cut the Italian Cornbread into 1-inch cubes, arrange on a baking sheet and drizzle lightly with olive oil. Bake to slightly crisp the bread without toasting it, 10 to 15 minutes. Set aside to cool.
In a small jar, shake together 1/4 cup olive oil, the vinegar and some salt and pepper.
Put the cooled cornbread and vegetables in a large bowl. Pour over the dressing, tossing gently to combine. Add the mozzarella balls and some salt and pepper and mix. Add the basil and toss again. Cover and allow to sit at room temperature for 1 to 2 hours before serving. Sprinkle with more salt and pepper and serve.
Preheat the oven to 450 degrees F.
Combine the cornmeal, flour, baking powder and salt in a bowl and stir together.
Measure the buttermilk and milk into a measuring cup and add the egg. Stir together with a fork. Add the baking soda and stir. Add the Parmesan, sun-dried tomatoes and oregano and mix together. Pour the milk mixture into the dry ingredients and stir with a fork until combined.
In a small microwave-safe bowl, melt 1/4 cup shortening in the microwave. Slowly add the melted shortening to the batter, stirring until just combined.
In a 10-inch cast-iron skillet, melt the remaining 2 tablespoons shortening over medium heat. Pour the batter into the hot skillet (the batter should sizzle) and spread to even out the surface. Cook on the stove top for 1 minute, then transfer to the oven and bake until golden brown, 20 to 25 minutes. The edges should be crispy!